Setup

1. Uva reef

Import Coral cover data

(Wide format)

# Read data 
  cover <- read.csv("CoverData/Uva_cover_R1.csv", header=TRUE, sep = ",")
  #summary(cover)
  
# Convert variables and factors to right format
  # convert to numeric variables
  cover$Pocillopora <- as.numeric(cover$Pocillopora) 
  cover$Massive <- as.numeric(cover$Other_scleractinians)
  cover$Millepora <- as.numeric(cover$Millepora) 
  cover$Algae<- as.numeric(cover$Algae)
  cover$Substrate<- as.numeric(cover$Substrate)
  cover$YEAR <- as.numeric(cover$YEAR)
  # convert to nominal factors
  cover$Location <- as.factor(cover$Location) 

# Dates   
  # Note: all day from a month were converted to the 15th  
  cover$Date<-as.Date(cover$Date, format =  "%Y-%m-%d")

  #summary(cover)
  str(cover)
## 'data.frame':    539 obs. of  112 variables:
##  $ YEAR                                   : num  1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 ...
##  $ Month                                  : Factor w/ 12 levels "Apr","Aug","Dec",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ Location                               : Factor w/ 3 levels "4x5","Uva_1m2",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ Transect                               : Factor w/ 12 levels "4x5","I","II",..: 2 3 4 5 6 7 8 9 10 11 ...
##  $ Date.of.Data.Collection.               : Factor w/ 76 levels "01/01/85","01/01/94",..: 75 75 75 75 75 75 75 75 75 75 ...
##  $ Date                                   : Date, format: "1980-12-15" "1980-12-15" ...
##  $ Depth.m.                               : int  2 2 2 2 2 2 2 2 2 2 ...
##  $ X.of.benth.points                      : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ X.of.subst.points                      : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ Analysis.by                            : Factor w/ 9 levels "","?","Peggy Fong",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ Date.of.Analysis                       : Factor w/ 9 levels "","04/04/17",..: NA NA NA NA NA NA NA NA NA NA ...
##  $ Processing                             : Factor w/ 7 levels "CPCe over Image",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Transect.Type                          : Factor w/ 4 levels "Estimated","Permanent",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ Method                                 : Factor w/ 3 levels "Chain_Transect",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Cycloceris.curvata..CCUR....coral      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Diaseris.distorta..DDIS....coral       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Gardineroseris.planulata..GPLA....coral: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Gpla_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Leptoseris.scabra..LSCA....coral       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.chiriquiensis..PCHI....coral    : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.clavus..PCLA....coral           : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.gigantea..PGIG....coral         : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pgig_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.maldivensis..PMAL....coral      : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.varians..PVAR....coral          : num  0 0 0 0 0 ...
##  $ Pvar_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pvar_Pale                              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pavona.spp..PAVO....coral              : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Porites.lobata..PLOB....coral          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Porites.panamensis..PPAN....coral      : num  0.137 0.137 0 0 0 ...
##  $ Ppan_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Psammocora.stellata..PSTE....coral     : num  0 0 0 0 0 ...
##  $ Psammocora.superficialis..PSUP....coral: num  0 0 0 0 0 ...
##  $ Psammocora.spp..PSAM....coral          : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.capitata..PCAP....coral    : num  3.288 0.959 9.178 4.11 0 ...
##  $ Pocillopora.damicornis..PDAM....coral  : num  3.151 2.603 0.411 2.877 1.781 ...
##  $ Pdam_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pdam_Pale                              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.effusus..PEFF....coral     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.elegans..PELE....coral     : num  17.4 0 0 0 0 ...
##  $ Pele_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pele_Pale                              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.eydouxi..PEYD....coral     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.inflata..PINF....coral     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.ligulata..PLIG....coral    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.meandrina..PMEA....coral   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.verrucosa..PVER....coral   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.woodjonesi..PWOO....coral  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Pocillopora.spp..POCI....coral         : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ RecMort                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Millepora.intricata..MINT....coral     : num  0 0 0 3.97 0 ...
##  $ Mint_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Millepora.platyphilla..MPLA....coral   : num  3.97 0 0 0 0 ...
##  $ Mpla_BL                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Astrangia.browni..ABRO....aherm        : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Astrangia.equatorialis..AEQU....aherm  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Caryophyllia.sp...CARYSPP....aherm     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Cladopsammia.eguchii..CEGU....aherm    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Cladopsammia.gracilis..CGRA....aherm   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Culicia.stellata..CSTE....aherm        : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Oulangia.bradleyi..OBRA....aherm       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Phyllangia.consagensis..PCON....aherm  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Polycyathus.isabela..PISA....aherm     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Rhizopsammia.verrilli..RVER....aherm   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Rhizopsammia.wellingtoni..RWEL....aherm: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tubastraea.coccinea..TCOC....aherm     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tubastraea.faulkneri..TFAU....aherm    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tubastraea.floreana..TFLO....aherm     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tubastraea.tagusensis..TTAG....aherm   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ BLCHCoral                              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Coral..C.                              : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Gorgonian..GO....go                    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Zoanthids..ZO....zo                    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Sponge..SPO....spo                     : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Antipathes.galapagensis..AGAL....bcoral: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Myriopathes.panamensis..MPAN....bcoral : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Balanus..BALA....O                     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Algmt                                  : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ AlgRub                                 : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Caulerpa..CAUL....maca                 : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Caulerpa_Feather.CSER.                 : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Caulerpa_Grape.CRAC.                   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Coralline.Algae..CALG....calg          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Filamentous.Cyanobacteria..FLCY....maca: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Laurencia                              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Macroalgae..MACA....maca               : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Peysonnelia                            : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Turf                                   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Other.Organism..O.                     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Dead.coral.w..turf.algae..DCA....dca   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Dead.Frame                             : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ DAMFR                                  : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ Boulder..B.                            : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Sand.Sediment..S.                      : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Rubble..R.                             : num  72.1 96.3 90.4 89 98.2 ...
##  $ Pavement..P.                           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Unknown..UNK.                          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ NA.LOSS                                : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ Tape.edge                              : num  0 0 0 0 0 0 0 0 0 0 ...
##   [list output truncated]

Check transects/sample units

Explore data

Pocillopora

  • Pre-1982 Pocillopora cover in 4*5 = 77% manually added
  • Line = mean
  • Boxplots = median

Non-Pocillopora scleractinians (Uva)

  • Line = mean
  • Boxplots = median

Millepora (Uva)

  • Millepora spp. (individual transects)

Data analysis (Aggregated data)

Aggregate data (Pocillopora)

  • Hierarchically aggregate by date and location
# Aggregate by Dataset - Month -Year
  aggr.location <- aggregate(Pocillopora 
                             ~YEAR+Month+Location,
                             FUN=mean, data=cover)
  
  aggr.location$Year_F<-as.factor(aggr.location$YEAR)
  aggr.location$Date<-paste(aggr.location$YEAR, aggr.location$Month, "15", sep = "-")
  aggr.location$Date<-as.Date(aggr.location$Date, format = "%Y-%b-%d")
  str(aggr.location)
## 'data.frame':    88 obs. of  6 variables:
##  $ YEAR       : num  2016 2017 1984 1985 2014 ...
##  $ Month      : Factor w/ 12 levels "Apr","Aug","Dec",..: 1 1 2 2 2 2 2 3 3 3 ...
##  $ Location   : Factor w/ 3 levels "4x5","Uva_1m2",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Pocillopora: num  57.28 71.659 0.242 0.62 73.07 ...
##  $ Year_F     : Factor w/ 29 levels "1980","1983",..: 27 28 3 4 25 26 29 1 3 9 ...
##  $ Date       : Date, format: "2016-04-15" "2017-04-15" ...
  #write.csv(aggr.location, 
   #       "Outputs/Pocillopora_mean_by_dataset.csv",
   #       row.names = F)

Stats Pocillopora for conceptual model (pooled datasets)

Pocillopora (model 0)

This model includes aggregated data from Chiriqui

  • Aggregated by location (Dataset)
  • YEAR is a continuous variable
  • Location (Dataset) as a random factor

  • Model is significant, but ignores high cover pre-1982

  • Data does not look normally distributed, which is ok, since the coral cover cannot be linear (Year as continuous), unless pre-1982 is removed?

** Do I need to change the intercept options?**

# # All years 1980_2018 
#   model0 <- lme(
#     Pocillopora ~ -1 + YEAR, random = ~1|Location, data=aggr.location)
#   summary(model0)
#   anova(model0)
#   
#   plot(ranef(model0))    # Symmetrical scatter effects around zero?
#   plot(model0)           # plot residuals vs fitted
#   resnorm1 <- resid(model0)
#   hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
#   coef.m1 <- as.data.frame(coef(summary(model0)))    # Coefficients of the model
#   
#   plot(model0, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
#   plot(model0, Pocillopora ~ fitted(.), abline = c(0,1))

#-----
  model0 <- lme(
  Pocillopora ~ YEAR, random = ~1|Location, data=aggr.location)
  summary(model0)
## Linear mixed-effects model fit by REML
##   Data: aggr.location 
##        AIC     BIC    logLik
##   725.0116 734.829 -358.5058
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    8.911826 14.02862
## 
## Fixed effects:  Pocillopora ~ YEAR 
##                  Value Std.Error DF   t-value p-value
## (Intercept) -3073.5862 277.08378 84 -11.09262       0
## YEAR            1.5485   0.13859 84  11.17316       0
##  Correlation: 
##      (Intr)
## YEAR -1    
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -1.1964839 -0.5889819 -0.2624917  0.4554009  5.4195389 
## 
## Number of Observations: 88
## Number of Groups: 3
  anova(model0)
  plot(ranef(model0))    # Symmetrical scatter effects around zero?
  plot(model0)           # plot residuals vs fitted
  resnorm1 <- resid(model0)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(model0)))    # Coefficients of the model
  
  plot(model0, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(model0, Pocillopora ~ fitted(.), abline = c(0,1))

Model 0 (data) plot vs (predicted values)

Model_0 <- ggplot(aggr.location, aes(x=YEAR, y=Pocillopora)) +
  stat_boxplot(aes(group=YEAR), geom = 'errorbar')+
  geom_point(aes(colour=Location))+
  geom_smooth(method = lm, se=FALSE, linetype = "dashed", colour="red")+
  geom_smooth(span = 0.3, se=T, colour="darkgray")+ 

  scale_y_continuous("Pocillopora cover (%)",
                      breaks = seq(0, 80, by=10),
                     limits = c(-2, 80),
                     expand = c(0,0))+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1980, 2018, by=2),
                     expand = c(0,0))+
  annotate("rect", xmin = 1982, xmax = 1983, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 1997, xmax = 1998, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 2015, xmax = 2016,
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  theme(legend.position = c(0.25, 0.8))+
  labs(title="Model 1 data")

Model 0

  • Extract model 1 predicted values
# Create a new data frame for independent variables  
NewData_0 <- expand.grid(Location=unique(aggr.location$Location),
                        YEAR=seq((min(aggr.location$YEAR)), (max(aggr.location$YEAR))))
pred_0 <- predict(model0 , newdata=NewData_0, level=0)
#summary(pred_0) 
#length(pred_0)
  • Plot model predictions
# Using model data 
  Model0_plot <- ggplot(aggr.location, 
                        aes(x=YEAR, y=Pocillopora, colour=Location)) +
      geom_point(aes(fill=factor(Location)),
                 shape = 21, colour = "black",
                 size = 2, stroke = 0.3, alpha=0.5) +
      
  scale_y_continuous("Pocillopora cover (%)", 
                     breaks = seq(0, 80, by=10), 
                     limits = c(-2, 80),
                     expand = c(0 ,0))+
  scale_x_continuous("", limits = c(1979, 2018),
                     breaks = seq(1980, 2018, by=2), 
                     expand = c(0.02,0.02))+
  
  geom_line(data=NewData_0, 
            aes(y=predict(model0, level=0, newdata=NewData_0)), size=2)+
  labs(title="Model 1 prediction")
  • Compare data and predictions
 Model0_All<-grid.arrange(Model_0, Model0_plot, ncol=2)

Pocillopora (model 0b: removing 1980 datapoints)

This model includes aggregated data from Chiriqui

  • Aggregated by location (Dataset)
  • YEAR is a continuous variable (1980 data removed)
  • Location (Dataset) as a random factor
aggr.locationb<-filter(aggr.location, YEAR>1983)
summary(aggr.locationb)
##       YEAR          Month           Location   Pocillopora          Year_F  
##  Min.   :1984   Mar    :22   4x5        :38   Min.   : 0.2145   1985   : 8  
##  1st Qu.:1988   Aug    :12   Uva_1m2    :18   1st Qu.: 1.5079   1984   : 7  
##  Median :1997   Jul    :10   UvRf-Chains:27   Median :12.9349   1997   : 5  
##  Mean   :1999   Feb    : 7                    Mean   :20.6385   1989   : 3  
##  3rd Qu.:2006   Jan    : 7                    3rd Qu.:33.5717   1990   : 3  
##  Max.   :2018   Apr    : 6                    Max.   :73.5546   1994   : 3  
##                 (Other):19                                      (Other):54  
##       Date           
##  Min.   :1984-06-15  
##  1st Qu.:1988-10-15  
##  Median :1997-10-15  
##  Mean   :1999-01-14  
##  3rd Qu.:2006-11-13  
##  Max.   :2018-08-15  
## 
  • Seems that removing the intercept is an issue…
# All years 1980_2018 

  model0b <- lme(
    Pocillopora ~ YEAR, random = ~1| Location, data=aggr.locationb)
  summary(model0b)
## Linear mixed-effects model fit by REML
##   Data: aggr.locationb 
##        AIC      BIC    logLik
##   630.7988 640.3766 -311.3994
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    10.05117 9.986885
## 
## Fixed effects:  Pocillopora ~ YEAR 
##                 Value Std.Error DF   t-value p-value
## (Intercept) -3648.888 211.14511 79 -17.28142       0
## YEAR            1.835   0.10554 79  17.38993       0
##  Correlation: 
##      (Intr)
## YEAR -1    
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -1.8626007 -0.5962037 -0.1968177  0.5313649  2.2762352 
## 
## Number of Observations: 83
## Number of Groups: 3
  anova(model0b)
  print(model0b)
## Linear mixed-effects model fit by REML
##   Data: aggr.locationb 
##   Log-restricted-likelihood: -311.3994
##   Fixed: Pocillopora ~ YEAR 
##  (Intercept)         YEAR 
## -3648.888298     1.835369 
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    10.05117 9.986885
## 
## Number of Observations: 83
## Number of Groups: 3
  plot(ranef(model0b))    # Symmetrical scatter effects around zero?
  plot(model0b)           # plot residuals vs fitted
  resnorm1 <- resid(model0b)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(model0b)))    # Coefficients of the model
  
  plot(model0b, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(model0b, Pocillopora ~ fitted(.), abline = c(0,1))

Model 0b (data) plot

Model 0b

  • Extract model 1b predicted values
# Create a new data frame for independent variables  
NewData_0b <- expand.grid(Location=unique(aggr.locationb$Location),
                        YEAR=seq((min(aggr.location$YEAR)), (max(aggr.locationb$YEAR))))
pred_0b <- predict(model0b, newdata=NewData_0b, level=0)
#summary(pred_0b) 
#length(pred_0b)
  • Plot model predictions
# Using model data 
  Model0_plotb <- ggplot(aggr.locationb, 
                        aes(x=YEAR, y=Pocillopora, colour=Location)) +
      geom_point(aes(fill=factor(Location)),
                 shape = 21, colour = "black",
                 size = 2, stroke = 0.3, alpha=0.5) +
      
  scale_y_continuous("Pocillopora cover (%)", 
                     breaks = seq(0, 80, by=10), 
                     limits = c(-2, 80))+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1980, 2018, by=2), 
                     expand = c(0.0,0.0))+

  geom_line(data=NewData_0b, 
            aes(y=predict(model0b, level=0, newdata=NewData_0b)), size=2)+
  labs(title="Model 1b prediction")

Model 0b (data) plot vs (predicted values)

 Model0b_All<-grid.arrange(Model_0b_data, Model0_plotb, ncol=2)

Pocillopora model 1 (+ multiple comparisons among years)

This model includes data from Chiriqui

  • Aggregated by location
  • Year is a factor
  • Location as a random factor

Results:

  • Model is significant
  • Better normality
model1_final <- lme(
    Pocillopora ~ -1 + Year_F, random = ~1|Location, data=aggr.location)
    summary(model1_final)
## Linear mixed-effects model fit by REML
##   Data: aggr.location 
##        AIC      BIC    logLik
##   553.5645 617.9682 -245.7823
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    10.55603 11.48019
## 
## Fixed effects:  Pocillopora ~ -1 + Year_F 
##               Value Std.Error DF   t-value p-value
## Year_F1980 44.29895 10.210061 57  4.338755  0.0001
## Year_F1983 16.57415  9.188955 57  1.803704  0.0766
## Year_F1984 -6.78593  7.632959 57 -0.889030  0.3777
## Year_F1985 -4.34381  7.439948 57 -0.583849  0.5616
## Year_F1986  1.02520 10.210061 57  0.100411  0.9204
## Year_F1987  1.27457 10.210061 57  0.124834  0.9011
## Year_F1988  2.23030 10.210061 57  0.218442  0.8279
## Year_F1989 -2.07795  9.083723 57 -0.228756  0.8199
## Year_F1990 -0.94790  9.083723 57 -0.104352  0.9173
## Year_F1992  4.16000 10.210061 57  0.407441  0.6852
## Year_F1993  4.83406 10.210061 57  0.473461  0.6377
## Year_F1994  3.94642  9.004154 57  0.438289  0.6628
## Year_F1995 10.16016  9.004154 57  1.128386  0.2639
## Year_F1997 13.98328  7.977199 57  1.752906  0.0850
## Year_F1998 15.45352 10.191919 57  1.516252  0.1350
## Year_F2000 19.65706  9.004154 57  2.183110  0.0332
## Year_F2001 20.71683 10.192208 57  2.032614  0.0468
## Year_F2002 29.00607  9.004154 57  3.221409  0.0021
## Year_F2003 31.38803  9.004154 57  3.485950  0.0010
## Year_F2004 36.30428 10.210061 57  3.555736  0.0008
## Year_F2005 34.95335  9.004154 57  3.881914  0.0003
## Year_F2006 43.60831 10.192208 57  4.278593  0.0001
## Year_F2007 38.34011  9.004154 57  4.258047  0.0001
## Year_F2010 43.32774  9.004154 57  4.811973  0.0000
## Year_F2014 46.40007  9.004154 57  5.153185  0.0000
## Year_F2015 47.75547  9.004154 57  5.303715  0.0000
## Year_F2016 40.01622  9.004154 57  4.444195  0.0000
## Year_F2017 54.79270  9.004154 57  6.085269  0.0000
## Year_F2018 56.34970  9.004154 57  6.258189  0.0000
##  Correlation: 
##            Y_F1980 Y_F1983 Y_F1984 Y_F1985 Y_F1986 Y_F1987 Y_F1988 Y_F1989
## Year_F1983 0.409                                                          
## Year_F1984 0.492   0.525                                                  
## Year_F1985 0.505   0.545   0.689                                          
## Year_F1986 0.368   0.409   0.492   0.505                                  
## Year_F1987 0.368   0.409   0.492   0.505   0.368                          
## Year_F1988 0.368   0.409   0.492   0.505   0.368   0.368                  
## Year_F1989 0.413   0.451   0.560   0.573   0.413   0.413   0.413          
## Year_F1990 0.413   0.451   0.560   0.573   0.413   0.413   0.413   0.468  
## Year_F1992 0.368   0.409   0.492   0.505   0.368   0.368   0.368   0.413  
## Year_F1993 0.368   0.409   0.492   0.505   0.368   0.368   0.368   0.413  
## Year_F1994 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F1995 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F1997 0.453   0.509   0.601   0.618   0.453   0.453   0.453   0.507  
## Year_F1998 0.351   0.402   0.460   0.475   0.351   0.351   0.351   0.391  
## Year_F2000 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2001 0.351   0.379   0.480   0.489   0.351   0.351   0.351   0.399  
## Year_F2002 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2003 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2004 0.368   0.409   0.492   0.505   0.368   0.368   0.368   0.413  
## Year_F2005 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2006 0.351   0.379   0.480   0.489   0.351   0.351   0.351   0.399  
## Year_F2007 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2010 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2014 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2015 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2016 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2017 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
## Year_F2018 0.404   0.449   0.540   0.554   0.404   0.404   0.404   0.454  
##            Y_F1990 Y_F1992 Y_F1993 Y_F1994 Y_F1995 Y_F1997 Y_F1998 Y_F2000
## Year_F1983                                                                
## Year_F1984                                                                
## Year_F1985                                                                
## Year_F1986                                                                
## Year_F1987                                                                
## Year_F1988                                                                
## Year_F1989                                                                
## Year_F1990                                                                
## Year_F1992 0.413                                                          
## Year_F1993 0.413   0.368                                                  
## Year_F1994 0.454   0.404   0.404                                          
## Year_F1995 0.454   0.404   0.404   0.458                                  
## Year_F1997 0.507   0.453   0.453   0.517   0.517                          
## Year_F1998 0.391   0.351   0.351   0.405   0.405   0.461                  
## Year_F2000 0.454   0.404   0.404   0.458   0.458   0.517   0.405          
## Year_F2001 0.399   0.351   0.351   0.405   0.405   0.456   0.355   0.405  
## Year_F2002 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2003 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2004 0.413   0.368   0.368   0.404   0.404   0.453   0.351   0.404  
## Year_F2005 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2006 0.399   0.351   0.351   0.405   0.405   0.456   0.355   0.405  
## Year_F2007 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2010 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2014 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2015 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2016 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2017 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
## Year_F2018 0.454   0.404   0.404   0.458   0.458   0.517   0.405   0.458  
##            Y_F2001 Y_F2002 Y_F2003 Y_F2004 Y_F2005 Y_F2006 Y_F2007 Y_F2010
## Year_F1983                                                                
## Year_F1984                                                                
## Year_F1985                                                                
## Year_F1986                                                                
## Year_F1987                                                                
## Year_F1988                                                                
## Year_F1989                                                                
## Year_F1990                                                                
## Year_F1992                                                                
## Year_F1993                                                                
## Year_F1994                                                                
## Year_F1995                                                                
## Year_F1997                                                                
## Year_F1998                                                                
## Year_F2000                                                                
## Year_F2001                                                                
## Year_F2002 0.405                                                          
## Year_F2003 0.405   0.458                                                  
## Year_F2004 0.351   0.404   0.404                                          
## Year_F2005 0.405   0.458   0.458   0.404                                  
## Year_F2006 0.366   0.405   0.405   0.351   0.405                          
## Year_F2007 0.405   0.458   0.458   0.404   0.458   0.405                  
## Year_F2010 0.405   0.458   0.458   0.404   0.458   0.405   0.458          
## Year_F2014 0.405   0.458   0.458   0.404   0.458   0.405   0.458   0.458  
## Year_F2015 0.405   0.458   0.458   0.404   0.458   0.405   0.458   0.458  
## Year_F2016 0.405   0.458   0.458   0.404   0.458   0.405   0.458   0.458  
## Year_F2017 0.405   0.458   0.458   0.404   0.458   0.405   0.458   0.458  
## Year_F2018 0.405   0.458   0.458   0.404   0.458   0.405   0.458   0.458  
##            Y_F2014 Y_F2015 Y_F2016 Y_F2017
## Year_F1983                                
## Year_F1984                                
## Year_F1985                                
## Year_F1986                                
## Year_F1987                                
## Year_F1988                                
## Year_F1989                                
## Year_F1990                                
## Year_F1992                                
## Year_F1993                                
## Year_F1994                                
## Year_F1995                                
## Year_F1997                                
## Year_F1998                                
## Year_F2000                                
## Year_F2001                                
## Year_F2002                                
## Year_F2003                                
## Year_F2004                                
## Year_F2005                                
## Year_F2006                                
## Year_F2007                                
## Year_F2010                                
## Year_F2014                                
## Year_F2015 0.458                          
## Year_F2016 0.458   0.458                  
## Year_F2017 0.458   0.458   0.458          
## Year_F2018 0.458   0.458   0.458   0.458  
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -1.9719022 -0.5347533 -0.1131969  0.6440439  1.9719022 
## 
## Number of Observations: 88
## Number of Groups: 3
    anova(model1_final)
  plot(ranef(model1_final))    # Symmetrical scatter effects around zero?
  plot(model1_final)           # plot residuals vs fitted
  resnorm1 <- resid(model1_final)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(model1_final)))    # Coefficients of the model
  
  plot(model1_final, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(model1_final, Pocillopora ~ fitted(.), abline = c(0,1))

# Multicomp emmeans
    Year_F.emm<-emmeans(model1_final, ~Year_F)
    #contrast(Year_F.emm, "tukey")
    year_groups<-cld(Year_F.emm, by=NULL) # compact-letter display
    year_groups<-year_groups[order(year_groups$Year_F),] 
    year_groups
    write.csv(year_groups, "Outputs/UvaPocilloTukey.csv", row.names = F)

Multiple comparisons among years

  • Too many lines!

Summary:

  • 1980 is different from 1983-2001) -> Coral cover lose after 1981-82 ENSO
  • “Recovery” by ~2002 (no differences between 1980 and 2002) uninterrupted until 2018 -> no significant cover loss in 1997-98 nor 2015-16
# Multicomp emmeans glht
  m.comp_Pocillopora <- glht(model1_final, linfct = mcp(Year_F = "Tukey"))
  Model1_multipcomp<-summary(m.comp_Pocillopora, test = univariate())
  Model1_multipcomp
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Fit: lme.formula(fixed = Pocillopora ~ -1 + Year_F, data = aggr.location, 
##     random = ~1 | Location)
## 
## Linear Hypotheses:
##                  Estimate Std. Error z value Pr(>|z|)    
## 1983 - 1980 == 0 -27.7248    10.5818  -2.620 0.008792 ** 
## 1984 - 1980 == 0 -51.0849     9.2639  -5.514 3.50e-08 ***
## 1985 - 1980 == 0 -48.6428     9.1054  -5.342 9.18e-08 ***
## 1986 - 1980 == 0 -43.2738    11.4802  -3.769 0.000164 ***
## 1987 - 1980 == 0 -43.0244    11.4802  -3.748 0.000178 ***
## 1988 - 1980 == 0 -42.0687    11.4802  -3.664 0.000248 ***
## 1989 - 1980 == 0 -46.3769    10.4913  -4.421 9.85e-06 ***
## 1990 - 1980 == 0 -45.2469    10.4913  -4.313 1.61e-05 ***
## 1992 - 1980 == 0 -40.1390    11.4802  -3.496 0.000472 ***
## 1993 - 1980 == 0 -39.4649    11.4802  -3.438 0.000587 ***
## 1994 - 1980 == 0 -40.3525    10.5373  -3.830 0.000128 ***
## 1995 - 1980 == 0 -34.1388    10.5373  -3.240 0.001196 ** 
## 1997 - 1980 == 0 -30.3157     9.6992  -3.126 0.001774 ** 
## 1998 - 1980 == 0 -28.8454    11.6204  -2.482 0.013053 *  
## 2000 - 1980 == 0 -24.6419    10.5373  -2.339 0.019359 *  
## 2001 - 1980 == 0 -23.5821    11.6211  -2.029 0.042433 *  
## 2002 - 1980 == 0 -15.2929    10.5373  -1.451 0.146692    
## 2003 - 1980 == 0 -12.9109    10.5373  -1.225 0.220476    
## 2004 - 1980 == 0  -7.9947    11.4802  -0.696 0.486185    
## 2005 - 1980 == 0  -9.3456    10.5373  -0.887 0.375127    
## 2006 - 1980 == 0  -0.6906    11.6211  -0.059 0.952610    
## 2007 - 1980 == 0  -5.9588    10.5373  -0.566 0.571732    
## 2010 - 1980 == 0  -0.9712    10.5373  -0.092 0.926564    
## 2014 - 1980 == 0   2.1011    10.5373   0.199 0.841950    
## 2015 - 1980 == 0   3.4565    10.5373   0.328 0.742891    
## 2016 - 1980 == 0  -4.2827    10.5373  -0.406 0.684421    
## 2017 - 1980 == 0  10.4938    10.5373   0.996 0.319313    
## 2018 - 1980 == 0  12.0507    10.5373   1.144 0.252776    
## 1984 - 1983 == 0 -23.3601     8.3105  -2.811 0.004940 ** 
## 1985 - 1983 == 0 -20.9180     8.0767  -2.590 0.009600 ** 
## 1986 - 1983 == 0 -15.5490    10.5818  -1.469 0.141723    
## 1987 - 1983 == 0 -15.2996    10.5818  -1.446 0.148222    
## 1988 - 1983 == 0 -14.3439    10.5818  -1.356 0.175252    
## 1989 - 1983 == 0 -18.6521     9.5748  -1.948 0.051411 .  
## 1990 - 1983 == 0 -17.5221     9.5748  -1.830 0.067248 .  
## 1992 - 1983 == 0 -12.4142    10.5818  -1.173 0.240731    
## 1993 - 1983 == 0 -11.7401    10.5818  -1.109 0.267232    
## 1994 - 1983 == 0 -12.6277     9.5512  -1.322 0.186131    
## 1995 - 1983 == 0  -6.4140     9.5512  -0.672 0.501877    
## 1997 - 1983 == 0  -2.5909     8.5680  -0.302 0.762354    
## 1998 - 1983 == 0  -1.1206    10.6341  -0.105 0.916073    
## 2000 - 1983 == 0   3.0829     9.5512   0.323 0.746864    
## 2001 - 1983 == 0   4.1427    10.8348   0.382 0.702204    
## 2002 - 1983 == 0  12.4319     9.5512   1.302 0.193050    
## 2003 - 1983 == 0  14.8139     9.5512   1.551 0.120902    
## 2004 - 1983 == 0  19.7301    10.5818   1.865 0.062247 .  
## 2005 - 1983 == 0  18.3792     9.5512   1.924 0.054319 .  
## 2006 - 1983 == 0  27.0342    10.8348   2.495 0.012592 *  
## 2007 - 1983 == 0  21.7660     9.5512   2.279 0.022675 *  
## 2010 - 1983 == 0  26.7536     9.5512   2.801 0.005093 ** 
## 2014 - 1983 == 0  29.8259     9.5512   3.123 0.001792 ** 
## 2015 - 1983 == 0  31.1813     9.5512   3.265 0.001096 ** 
## 2016 - 1983 == 0  23.4421     9.5512   2.454 0.014114 *  
## 2017 - 1983 == 0  38.2185     9.5512   4.001 6.30e-05 ***
## 2018 - 1983 == 0  39.7755     9.5512   4.164 3.12e-05 ***
## 1985 - 1984 == 0   2.4421     5.9498   0.410 0.681475    
## 1986 - 1984 == 0   7.8111     9.2639   0.843 0.399128    
## 1987 - 1984 == 0   8.0605     9.2639   0.870 0.384247    
## 1988 - 1984 == 0   9.0162     9.2639   0.973 0.330421    
## 1989 - 1984 == 0   4.7080     7.9417   0.593 0.553304    
## 1990 - 1984 == 0   5.8380     7.9417   0.735 0.462273    
## 1992 - 1984 == 0  10.9459     9.2639   1.182 0.237377    
## 1993 - 1984 == 0  11.6200     9.2639   1.254 0.209722    
## 1994 - 1984 == 0  10.7324     8.0654   1.331 0.183298    
## 1995 - 1984 == 0  16.9461     8.0654   2.101 0.035633 *  
## 1997 - 1984 == 0  20.7692     6.9787   2.976 0.002920 ** 
## 1998 - 1984 == 0  22.2394     9.5173   2.337 0.019452 *  
## 2000 - 1984 == 0  26.4430     8.0654   3.279 0.001043 ** 
## 2001 - 1984 == 0  27.5028     9.3558   2.940 0.003286 ** 
## 2002 - 1984 == 0  35.7920     8.0654   4.438 9.09e-06 ***
## 2003 - 1984 == 0  38.1740     8.0654   4.733 2.21e-06 ***
## 2004 - 1984 == 0  43.0902     9.2639   4.651 3.30e-06 ***
## 2005 - 1984 == 0  41.7393     8.0654   5.175 2.28e-07 ***
## 2006 - 1984 == 0  50.3942     9.3558   5.386 7.19e-08 ***
## 2007 - 1984 == 0  45.1260     8.0654   5.595 2.21e-08 ***
## 2010 - 1984 == 0  50.1137     8.0654   6.213 5.18e-10 ***
## 2014 - 1984 == 0  53.1860     8.0654   6.594 4.27e-11 ***
## 2015 - 1984 == 0  54.5414     8.0654   6.762 1.36e-11 ***
## 2016 - 1984 == 0  46.8021     8.0654   5.803 6.52e-09 ***
## 2017 - 1984 == 0  61.5786     8.0654   7.635 2.26e-14 ***
## 2018 - 1984 == 0  63.1356     8.0654   7.828 4.88e-15 ***
## 1986 - 1985 == 0   5.3690     9.1054   0.590 0.555424    
## 1987 - 1985 == 0   5.6184     9.1054   0.617 0.537209    
## 1988 - 1985 == 0   6.5741     9.1054   0.722 0.470293    
## 1989 - 1985 == 0   2.2659     7.7760   0.291 0.770751    
## 1990 - 1985 == 0   3.3959     7.7760   0.437 0.662316    
## 1992 - 1985 == 0   8.5038     9.1054   0.934 0.350339    
## 1993 - 1985 == 0   9.1779     9.1054   1.008 0.313473    
## 1994 - 1985 == 0   8.2902     7.8830   1.052 0.292954    
## 1995 - 1985 == 0  14.5040     7.8830   1.840 0.065781 .  
## 1997 - 1985 == 0  18.3271     6.7535   2.714 0.006653 ** 
## 1998 - 1985 == 0  19.7973     9.3386   2.120 0.034012 *  
## 2000 - 1985 == 0  24.0009     7.8830   3.045 0.002330 ** 
## 2001 - 1985 == 0  25.0606     9.2240   2.717 0.006590 ** 
## 2002 - 1985 == 0  33.3499     7.8830   4.231 2.33e-05 ***
## 2003 - 1985 == 0  35.7318     7.8830   4.533 5.82e-06 ***
## 2004 - 1985 == 0  40.6481     9.1054   4.464 8.04e-06 ***
## 2005 - 1985 == 0  39.2972     7.8830   4.985 6.19e-07 ***
## 2006 - 1985 == 0  47.9521     9.2240   5.199 2.01e-07 ***
## 2007 - 1985 == 0  42.6839     7.8830   5.415 6.14e-08 ***
## 2010 - 1985 == 0  47.6716     7.8830   6.047 1.47e-09 ***
## 2014 - 1985 == 0  50.7439     7.8830   6.437 1.22e-10 ***
## 2015 - 1985 == 0  52.0993     7.8830   6.609 3.87e-11 ***
## 2016 - 1985 == 0  44.3600     7.8830   5.627 1.83e-08 ***
## 2017 - 1985 == 0  59.1365     7.8830   7.502 6.28e-14 ***
## 2018 - 1985 == 0  60.6935     7.8830   7.699 1.38e-14 ***
## 1987 - 1986 == 0   0.2494    11.4802   0.022 0.982670    
## 1988 - 1986 == 0   1.2051    11.4802   0.105 0.916398    
## 1989 - 1986 == 0  -3.1032    10.4913  -0.296 0.767395    
## 1990 - 1986 == 0  -1.9731    10.4913  -0.188 0.850822    
## 1992 - 1986 == 0   3.1348    11.4802   0.273 0.784806    
## 1993 - 1986 == 0   3.8089    11.4802   0.332 0.740057    
## 1994 - 1986 == 0   2.9212    10.5373   0.277 0.781605    
## 1995 - 1986 == 0   9.1350    10.5373   0.867 0.385986    
## 1997 - 1986 == 0  12.9581     9.6992   1.336 0.181550    
## 1998 - 1986 == 0  14.4283    11.6204   1.242 0.214369    
## 2000 - 1986 == 0  18.6319    10.5373   1.768 0.077029 .  
## 2001 - 1986 == 0  19.6916    11.6211   1.694 0.090176 .  
## 2002 - 1986 == 0  27.9809    10.5373   2.655 0.007921 ** 
## 2003 - 1986 == 0  30.3628    10.5373   2.881 0.003958 ** 
## 2004 - 1986 == 0  35.2791    11.4802   3.073 0.002119 ** 
## 2005 - 1986 == 0  33.9282    10.5373   3.220 0.001283 ** 
## 2006 - 1986 == 0  42.5831    11.6211   3.664 0.000248 ***
## 2007 - 1986 == 0  37.3149    10.5373   3.541 0.000398 ***
## 2010 - 1986 == 0  42.3025    10.5373   4.015 5.96e-05 ***
## 2014 - 1986 == 0  45.3749    10.5373   4.306 1.66e-05 ***
## 2015 - 1986 == 0  46.7303    10.5373   4.435 9.22e-06 ***
## 2016 - 1986 == 0  38.9910    10.5373   3.700 0.000215 ***
## 2017 - 1986 == 0  53.7675    10.5373   5.103 3.35e-07 ***
## 2018 - 1986 == 0  55.3245    10.5373   5.250 1.52e-07 ***
## 1988 - 1987 == 0   0.9557    11.4802   0.083 0.933652    
## 1989 - 1987 == 0  -3.3525    10.4913  -0.320 0.749308    
## 1990 - 1987 == 0  -2.2225    10.4913  -0.212 0.832232    
## 1992 - 1987 == 0   2.8854    11.4802   0.251 0.801551    
## 1993 - 1987 == 0   3.5595    11.4802   0.310 0.756519    
## 1994 - 1987 == 0   2.6719    10.5373   0.254 0.799833    
## 1995 - 1987 == 0   8.8856    10.5373   0.843 0.399086    
## 1997 - 1987 == 0  12.7087     9.6992   1.310 0.190099    
## 1998 - 1987 == 0  14.1790    11.6204   1.220 0.222396    
## 2000 - 1987 == 0  18.3825    10.5373   1.745 0.081068 .  
## 2001 - 1987 == 0  19.4423    11.6211   1.673 0.094325 .  
## 2002 - 1987 == 0  27.7315    10.5373   2.632 0.008494 ** 
## 2003 - 1987 == 0  30.1135    10.5373   2.858 0.004266 ** 
## 2004 - 1987 == 0  35.0297    11.4802   3.051 0.002278 ** 
## 2005 - 1987 == 0  33.6788    10.5373   3.196 0.001393 ** 
## 2006 - 1987 == 0  42.3337    11.6211   3.643 0.000270 ***
## 2007 - 1987 == 0  37.0655    10.5373   3.518 0.000436 ***
## 2010 - 1987 == 0  42.0532    10.5373   3.991 6.58e-05 ***
## 2014 - 1987 == 0  45.1255    10.5373   4.282 1.85e-05 ***
## 2015 - 1987 == 0  46.4809    10.5373   4.411 1.03e-05 ***
## 2016 - 1987 == 0  38.7417    10.5373   3.677 0.000236 ***
## 2017 - 1987 == 0  53.5181    10.5373   5.079 3.80e-07 ***
## 2018 - 1987 == 0  55.0751    10.5373   5.227 1.73e-07 ***
## 1989 - 1988 == 0  -4.3083    10.4913  -0.411 0.681329    
## 1990 - 1988 == 0  -3.1782    10.4913  -0.303 0.761937    
## 1992 - 1988 == 0   1.9297    11.4802   0.168 0.866513    
## 1993 - 1988 == 0   2.6038    11.4802   0.227 0.820576    
## 1994 - 1988 == 0   1.7161    10.5373   0.163 0.870627    
## 1995 - 1988 == 0   7.9299    10.5373   0.753 0.451718    
## 1997 - 1988 == 0  11.7530     9.6992   1.212 0.225608    
## 1998 - 1988 == 0  13.2232    11.6204   1.138 0.255148    
## 2000 - 1988 == 0  17.4268    10.5373   1.654 0.098163 .  
## 2001 - 1988 == 0  18.4865    11.6211   1.591 0.111662    
## 2002 - 1988 == 0  26.7758    10.5373   2.541 0.011052 *  
## 2003 - 1988 == 0  29.1577    10.5373   2.767 0.005656 ** 
## 2004 - 1988 == 0  34.0740    11.4802   2.968 0.002997 ** 
## 2005 - 1988 == 0  32.7230    10.5373   3.105 0.001900 ** 
## 2006 - 1988 == 0  41.3780    11.6211   3.561 0.000370 ***
## 2007 - 1988 == 0  36.1098    10.5373   3.427 0.000611 ***
## 2010 - 1988 == 0  41.0974    10.5373   3.900 9.61e-05 ***
## 2014 - 1988 == 0  44.1698    10.5373   4.192 2.77e-05 ***
## 2015 - 1988 == 0  45.5252    10.5373   4.320 1.56e-05 ***
## 2016 - 1988 == 0  37.7859    10.5373   3.586 0.000336 ***
## 2017 - 1988 == 0  52.5624    10.5373   4.988 6.09e-07 ***
## 2018 - 1988 == 0  54.1194    10.5373   5.136 2.81e-07 ***
## 1990 - 1989 == 0   1.1301     9.3735   0.121 0.904041    
## 1992 - 1989 == 0   6.2380    10.4913   0.595 0.552122    
## 1993 - 1989 == 0   6.9120    10.4913   0.659 0.510003    
## 1994 - 1989 == 0   6.0244     9.4500   0.638 0.523799    
## 1995 - 1989 == 0  12.2381     9.4500   1.295 0.195307    
## 1997 - 1989 == 0  16.0612     8.5222   1.885 0.059480 .  
## 1998 - 1989 == 0  17.5315    10.6778   1.642 0.100618    
## 2000 - 1989 == 0  21.7350     9.4500   2.300 0.021448 *  
## 2001 - 1989 == 0  22.7948    10.6114   2.148 0.031703 *  
## 2002 - 1989 == 0  31.0840     9.4500   3.289 0.001004 ** 
## 2003 - 1989 == 0  33.4660     9.4500   3.541 0.000398 ***
## 2004 - 1989 == 0  38.3822    10.4913   3.658 0.000254 ***
## 2005 - 1989 == 0  37.0313     9.4500   3.919 8.90e-05 ***
## 2006 - 1989 == 0  45.6863    10.6114   4.305 1.67e-05 ***
## 2007 - 1989 == 0  40.4181     9.4500   4.277 1.89e-05 ***
## 2010 - 1989 == 0  45.4057     9.4500   4.805 1.55e-06 ***
## 2014 - 1989 == 0  48.4780     9.4500   5.130 2.90e-07 ***
## 2015 - 1989 == 0  49.8334     9.4500   5.273 1.34e-07 ***
## 2016 - 1989 == 0  42.0942     9.4500   4.454 8.41e-06 ***
## 2017 - 1989 == 0  56.8707     9.4500   6.018 1.77e-09 ***
## 2018 - 1989 == 0  58.4277     9.4500   6.183 6.30e-10 ***
## 1992 - 1990 == 0   5.1079    10.4913   0.487 0.626350    
## 1993 - 1990 == 0   5.7820    10.4913   0.551 0.581551    
## 1994 - 1990 == 0   4.8943     9.4500   0.518 0.604515    
## 1995 - 1990 == 0  11.1081     9.4500   1.175 0.239812    
## 1997 - 1990 == 0  14.9312     8.5222   1.752 0.079768 .  
## 1998 - 1990 == 0  16.4014    10.6778   1.536 0.124530    
## 2000 - 1990 == 0  20.6050     9.4500   2.180 0.029226 *  
## 2001 - 1990 == 0  21.6647    10.6114   2.042 0.041187 *  
## 2002 - 1990 == 0  29.9540     9.4500   3.170 0.001526 ** 
## 2003 - 1990 == 0  32.3359     9.4500   3.422 0.000622 ***
## 2004 - 1990 == 0  37.2522    10.4913   3.551 0.000384 ***
## 2005 - 1990 == 0  35.9013     9.4500   3.799 0.000145 ***
## 2006 - 1990 == 0  44.5562    10.6114   4.199 2.68e-05 ***
## 2007 - 1990 == 0  39.2880     9.4500   4.157 3.22e-05 ***
## 2010 - 1990 == 0  44.2756     9.4500   4.685 2.80e-06 ***
## 2014 - 1990 == 0  47.3480     9.4500   5.010 5.43e-07 ***
## 2015 - 1990 == 0  48.7034     9.4500   5.154 2.55e-07 ***
## 2016 - 1990 == 0  40.9641     9.4500   4.335 1.46e-05 ***
## 2017 - 1990 == 0  55.7406     9.4500   5.898 3.67e-09 ***
## 2018 - 1990 == 0  57.2976     9.4500   6.063 1.33e-09 ***
## 1993 - 1992 == 0   0.6741    11.4802   0.059 0.953179    
## 1994 - 1992 == 0  -0.2136    10.5373  -0.020 0.983829    
## 1995 - 1992 == 0   6.0002    10.5373   0.569 0.569069    
## 1997 - 1992 == 0   9.8233     9.6992   1.013 0.311158    
## 1998 - 1992 == 0  11.2935    11.6204   0.972 0.331114    
## 2000 - 1992 == 0  15.4971    10.5373   1.471 0.141374    
## 2001 - 1992 == 0  16.5568    11.6211   1.425 0.154239    
## 2002 - 1992 == 0  24.8461    10.5373   2.358 0.018377 *  
## 2003 - 1992 == 0  27.2280    10.5373   2.584 0.009767 ** 
## 2004 - 1992 == 0  32.1443    11.4802   2.800 0.005111 ** 
## 2005 - 1992 == 0  30.7934    10.5373   2.922 0.003474 ** 
## 2006 - 1992 == 0  39.4483    11.6211   3.395 0.000687 ***
## 2007 - 1992 == 0  34.1801    10.5373   3.244 0.001180 ** 
## 2010 - 1992 == 0  39.1677    10.5373   3.717 0.000202 ***
## 2014 - 1992 == 0  42.2401    10.5373   4.009 6.11e-05 ***
## 2015 - 1992 == 0  43.5955    10.5373   4.137 3.51e-05 ***
## 2016 - 1992 == 0  35.8562    10.5373   3.403 0.000667 ***
## 2017 - 1992 == 0  50.6327    10.5373   4.805 1.55e-06 ***
## 2018 - 1992 == 0  52.1897    10.5373   4.953 7.31e-07 ***
## 1994 - 1993 == 0  -0.8876    10.5373  -0.084 0.932867    
## 1995 - 1993 == 0   5.3261    10.5373   0.505 0.613240    
## 1997 - 1993 == 0   9.1492     9.6992   0.943 0.345529    
## 1998 - 1993 == 0  10.6195    11.6204   0.914 0.360788    
## 2000 - 1993 == 0  14.8230    10.5373   1.407 0.159510    
## 2001 - 1993 == 0  15.8828    11.6211   1.367 0.171715    
## 2002 - 1993 == 0  24.1720    10.5373   2.294 0.021793 *  
## 2003 - 1993 == 0  26.5540    10.5373   2.520 0.011735 *  
## 2004 - 1993 == 0  31.4702    11.4802   2.741 0.006120 ** 
## 2005 - 1993 == 0  30.1193    10.5373   2.858 0.004258 ** 
## 2006 - 1993 == 0  38.7742    11.6211   3.337 0.000848 ***
## 2007 - 1993 == 0  33.5060    10.5373   3.180 0.001474 ** 
## 2010 - 1993 == 0  38.4937    10.5373   3.653 0.000259 ***
## 2014 - 1993 == 0  41.5660    10.5373   3.945 7.99e-05 ***
## 2015 - 1993 == 0  42.9214    10.5373   4.073 4.64e-05 ***
## 2016 - 1993 == 0  35.1822    10.5373   3.339 0.000841 ***
## 2017 - 1993 == 0  49.9586    10.5373   4.741 2.13e-06 ***
## 2018 - 1993 == 0  51.5156    10.5373   4.889 1.01e-06 ***
## 1995 - 1994 == 0   6.2137     9.3735   0.663 0.507393    
## 1997 - 1994 == 0  10.0369     8.3919   1.196 0.231690    
## 1998 - 1994 == 0  11.5071    10.5197   1.094 0.274015    
## 2000 - 1994 == 0  15.7106     9.3735   1.676 0.093726 .  
## 2001 - 1994 == 0  16.7704    10.5200   1.594 0.110902    
## 2002 - 1994 == 0  25.0596     9.3735   2.673 0.007508 ** 
## 2003 - 1994 == 0  27.4416     9.3735   2.928 0.003416 ** 
## 2004 - 1994 == 0  32.3579    10.5373   3.071 0.002135 ** 
## 2005 - 1994 == 0  31.0069     9.3735   3.308 0.000940 ***
## 2006 - 1994 == 0  39.6619    10.5200   3.770 0.000163 ***
## 2007 - 1994 == 0  34.3937     9.3735   3.669 0.000243 ***
## 2010 - 1994 == 0  39.3813     9.3735   4.201 2.65e-05 ***
## 2014 - 1994 == 0  42.4537     9.3735   4.529 5.92e-06 ***
## 2015 - 1994 == 0  43.8090     9.3735   4.674 2.96e-06 ***
## 2016 - 1994 == 0  36.0698     9.3735   3.848 0.000119 ***
## 2017 - 1994 == 0  50.8463     9.3735   5.424 5.81e-08 ***
## 2018 - 1994 == 0  52.4033     9.3735   5.591 2.26e-08 ***
## 1997 - 1995 == 0   3.8231     8.3919   0.456 0.648698    
## 1998 - 1995 == 0   5.2934    10.5197   0.503 0.614833    
## 2000 - 1995 == 0   9.4969     9.3735   1.013 0.310983    
## 2001 - 1995 == 0  10.5567    10.5200   1.003 0.315625    
## 2002 - 1995 == 0  18.8459     9.3735   2.011 0.044374 *  
## 2003 - 1995 == 0  21.2279     9.3735   2.265 0.023534 *  
## 2004 - 1995 == 0  26.1441    10.5373   2.481 0.013097 *  
## 2005 - 1995 == 0  24.7932     9.3735   2.645 0.008169 ** 
## 2006 - 1995 == 0  33.4482    10.5200   3.179 0.001475 ** 
## 2007 - 1995 == 0  28.1800     9.3735   3.006 0.002644 ** 
## 2010 - 1995 == 0  33.1676     9.3735   3.538 0.000403 ***
## 2014 - 1995 == 0  36.2399     9.3735   3.866 0.000111 ***
## 2015 - 1995 == 0  37.5953     9.3735   4.011 6.05e-05 ***
## 2016 - 1995 == 0  29.8561     9.3735   3.185 0.001447 ** 
## 2017 - 1995 == 0  44.6325     9.3735   4.762 1.92e-06 ***
## 2018 - 1995 == 0  46.1895     9.3735   4.928 8.32e-07 ***
## 1998 - 1997 == 0   1.4702     9.6206   0.153 0.878539    
## 2000 - 1997 == 0   5.6738     8.3919   0.676 0.498976    
## 2001 - 1997 == 0   6.7335     9.6653   0.697 0.486009    
## 2002 - 1997 == 0  15.0228     8.3919   1.790 0.073429 .  
## 2003 - 1997 == 0  17.4048     8.3919   2.074 0.038080 *  
## 2004 - 1997 == 0  22.3210     9.6992   2.301 0.021373 *  
## 2005 - 1997 == 0  20.9701     8.3919   2.499 0.012460 *  
## 2006 - 1997 == 0  29.6250     9.6653   3.065 0.002176 ** 
## 2007 - 1997 == 0  24.3568     8.3919   2.902 0.003703 ** 
## 2010 - 1997 == 0  29.3445     8.3919   3.497 0.000471 ***
## 2014 - 1997 == 0  32.4168     8.3919   3.863 0.000112 ***
## 2015 - 1997 == 0  33.7722     8.3919   4.024 5.71e-05 ***
## 2016 - 1997 == 0  26.0329     8.3919   3.102 0.001921 ** 
## 2017 - 1997 == 0  40.8094     8.3919   4.863 1.16e-06 ***
## 2018 - 1997 == 0  42.3664     8.3919   5.048 4.45e-07 ***
## 2000 - 1998 == 0   4.2035    10.5197   0.400 0.689460    
## 2001 - 1998 == 0   5.2633    11.5733   0.455 0.649266    
## 2002 - 1998 == 0  13.5526    10.5197   1.288 0.197640    
## 2003 - 1998 == 0  15.9345    10.5197   1.515 0.129840    
## 2004 - 1998 == 0  20.8508    11.6204   1.794 0.072761 .  
## 2005 - 1998 == 0  19.4998    10.5197   1.854 0.063789 .  
## 2006 - 1998 == 0  28.1548    11.5733   2.433 0.014985 *  
## 2007 - 1998 == 0  22.8866    10.5197   2.176 0.029585 *  
## 2010 - 1998 == 0  27.8742    10.5197   2.650 0.008056 ** 
## 2014 - 1998 == 0  30.9466    10.5197   2.942 0.003263 ** 
## 2015 - 1998 == 0  32.3019    10.5197   3.071 0.002136 ** 
## 2016 - 1998 == 0  24.5627    10.5197   2.335 0.019547 *  
## 2017 - 1998 == 0  39.3392    10.5197   3.740 0.000184 ***
## 2018 - 1998 == 0  40.8962    10.5197   3.888 0.000101 ***
## 2001 - 2000 == 0   1.0598    10.5200   0.101 0.919758    
## 2002 - 2000 == 0   9.3490     9.3735   0.997 0.318578    
## 2003 - 2000 == 0  11.7310     9.3735   1.251 0.210752    
## 2004 - 2000 == 0  16.6472    10.5373   1.580 0.114142    
## 2005 - 2000 == 0  15.2963     9.3735   1.632 0.102709    
## 2006 - 2000 == 0  23.9513    10.5200   2.277 0.022801 *  
## 2007 - 2000 == 0  18.6831     9.3735   1.993 0.046243 *  
## 2010 - 2000 == 0  23.6707     9.3735   2.525 0.011561 *  
## 2014 - 2000 == 0  26.7430     9.3735   2.853 0.004330 ** 
## 2015 - 2000 == 0  28.0984     9.3735   2.998 0.002721 ** 
## 2016 - 2000 == 0  20.3592     9.3735   2.172 0.029857 *  
## 2017 - 2000 == 0  35.1356     9.3735   3.748 0.000178 ***
## 2018 - 2000 == 0  36.6926     9.3735   3.914 9.06e-05 ***
## 2002 - 2001 == 0   8.2892    10.5200   0.788 0.430724    
## 2003 - 2001 == 0  10.6712    10.5200   1.014 0.310403    
## 2004 - 2001 == 0  15.5875    11.6211   1.341 0.179822    
## 2005 - 2001 == 0  14.2365    10.5200   1.353 0.175964    
## 2006 - 2001 == 0  22.8915    11.4802   1.994 0.046152 *  
## 2007 - 2001 == 0  17.6233    10.5200   1.675 0.093890 .  
## 2010 - 2001 == 0  22.6109    10.5200   2.149 0.031608 *  
## 2014 - 2001 == 0  25.6832    10.5200   2.441 0.014631 *  
## 2015 - 2001 == 0  27.0386    10.5200   2.570 0.010163 *  
## 2016 - 2001 == 0  19.2994    10.5200   1.835 0.066572 .  
## 2017 - 2001 == 0  34.0759    10.5200   3.239 0.001199 ** 
## 2018 - 2001 == 0  35.6329    10.5200   3.387 0.000706 ***
## 2003 - 2002 == 0   2.3820     9.3735   0.254 0.799406    
## 2004 - 2002 == 0   7.2982    10.5373   0.693 0.488554    
## 2005 - 2002 == 0   5.9473     9.3735   0.634 0.525770    
## 2006 - 2002 == 0  14.6022    10.5200   1.388 0.165121    
## 2007 - 2002 == 0   9.3340     9.3735   0.996 0.319354    
## 2010 - 2002 == 0  14.3217     9.3735   1.528 0.126541    
## 2014 - 2002 == 0  17.3940     9.3735   1.856 0.063503 .  
## 2015 - 2002 == 0  18.7494     9.3735   2.000 0.045473 *  
## 2016 - 2002 == 0  11.0102     9.3735   1.175 0.240155    
## 2017 - 2002 == 0  25.7866     9.3735   2.751 0.005941 ** 
## 2018 - 2002 == 0  27.3436     9.3735   2.917 0.003533 ** 
## 2004 - 2003 == 0   4.9162    10.5373   0.467 0.640816    
## 2005 - 2003 == 0   3.5653     9.3735   0.380 0.703678    
## 2006 - 2003 == 0  12.2203    10.5200   1.162 0.245386    
## 2007 - 2003 == 0   6.9521     9.3735   0.742 0.458287    
## 2010 - 2003 == 0  11.9397     9.3735   1.274 0.202745    
## 2014 - 2003 == 0  15.0120     9.3735   1.602 0.109259    
## 2015 - 2003 == 0  16.3674     9.3735   1.746 0.080788 .  
## 2016 - 2003 == 0   8.6282     9.3735   0.920 0.357320    
## 2017 - 2003 == 0  23.4047     9.3735   2.497 0.012529 *  
## 2018 - 2003 == 0  24.9617     9.3735   2.663 0.007745 ** 
## 2005 - 2004 == 0  -1.3509    10.5373  -0.128 0.897987    
## 2006 - 2004 == 0   7.3040    11.6211   0.629 0.529668    
## 2007 - 2004 == 0   2.0358    10.5373   0.193 0.846800    
## 2010 - 2004 == 0   7.0235    10.5373   0.667 0.505068    
## 2014 - 2004 == 0  10.0958    10.5373   0.958 0.338010    
## 2015 - 2004 == 0  11.4512    10.5373   1.087 0.277155    
## 2016 - 2004 == 0   3.7119    10.5373   0.352 0.724637    
## 2017 - 2004 == 0  18.4884    10.5373   1.755 0.079332 .  
## 2018 - 2004 == 0  20.0454    10.5373   1.902 0.057127 .  
## 2006 - 2005 == 0   8.6550    10.5200   0.823 0.410668    
## 2007 - 2005 == 0   3.3868     9.3735   0.361 0.717867    
## 2010 - 2005 == 0   8.3744     9.3735   0.893 0.371639    
## 2014 - 2005 == 0  11.4467     9.3735   1.221 0.222020    
## 2015 - 2005 == 0  12.8021     9.3735   1.366 0.172010    
## 2016 - 2005 == 0   5.0629     9.3735   0.540 0.589112    
## 2017 - 2005 == 0  19.8394     9.3735   2.117 0.034300 *  
## 2018 - 2005 == 0  21.3963     9.3735   2.283 0.022452 *  
## 2007 - 2006 == 0  -5.2682    10.5200  -0.501 0.616525    
## 2010 - 2006 == 0  -0.2806    10.5200  -0.027 0.978723    
## 2014 - 2006 == 0   2.7918    10.5200   0.265 0.790718    
## 2015 - 2006 == 0   4.1472    10.5200   0.394 0.693420    
## 2016 - 2006 == 0  -3.5921    10.5200  -0.341 0.732761    
## 2017 - 2006 == 0  11.1844    10.5200   1.063 0.287710    
## 2018 - 2006 == 0  12.7414    10.5200   1.211 0.225833    
## 2010 - 2007 == 0   4.9876     9.3735   0.532 0.594659    
## 2014 - 2007 == 0   8.0600     9.3735   0.860 0.389864    
## 2015 - 2007 == 0   9.4154     9.3735   1.004 0.315156    
## 2016 - 2007 == 0   1.6761     9.3735   0.179 0.858085    
## 2017 - 2007 == 0  16.4526     9.3735   1.755 0.079222 .  
## 2018 - 2007 == 0  18.0096     9.3735   1.921 0.054691 .  
## 2014 - 2010 == 0   3.0723     9.3735   0.328 0.743088    
## 2015 - 2010 == 0   4.4277     9.3735   0.472 0.636667    
## 2016 - 2010 == 0  -3.3115     9.3735  -0.353 0.723875    
## 2017 - 2010 == 0  11.4650     9.3735   1.223 0.221284    
## 2018 - 2010 == 0  13.0220     9.3735   1.389 0.164764    
## 2015 - 2014 == 0   1.3554     9.3735   0.145 0.885028    
## 2016 - 2014 == 0  -6.3839     9.3735  -0.681 0.495839    
## 2017 - 2014 == 0   8.3926     9.3735   0.895 0.370598    
## 2018 - 2014 == 0   9.9496     9.3735   1.061 0.288481    
## 2016 - 2015 == 0  -7.7392     9.3735  -0.826 0.409003    
## 2017 - 2015 == 0   7.0372     9.3735   0.751 0.452799    
## 2018 - 2015 == 0   8.5942     9.3735   0.917 0.359215    
## 2017 - 2016 == 0  14.7765     9.3735   1.576 0.114933    
## 2018 - 2016 == 0  16.3335     9.3735   1.743 0.081419 .  
## 2018 - 2017 == 0   1.5570     9.3735   0.166 0.868074    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Figure 1b: Pocillopora coral cover

Model 1 plot (data)

Model1_data <- ggplot(aggr.location, aes(x=YEAR, y=Pocillopora)) +
  geom_boxplot(aes(group=YEAR), outlier.shape = NA) +
  stat_boxplot(aes(group=YEAR), geom = 'errorbar')+
 geom_point(aes(fill=factor(Location)),
                 shape = 21, colour = "black",
                 size = 2, stroke = 0.8, alpha=0.5) +
  stat_summary(fun=mean, geom="line", colour="gray")+

  scale_y_continuous("Pocillopora spp. cover (%)", limits = c(-2, 80),
                     breaks = seq(-0, 80, by=10),
                     expand = c(0,0))+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1980, 2018, by=2), expand = c(0,0))+

  annotate("rect", xmin = 1983, xmax = 1984, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 1997.5, xmax = 1998.5, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 2015.5, xmax = 2016.5,
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  #ggtitle("Model 2 data")+
  theme(legend.position = c(0.25, 0.8))
Model1_data

#ggsave(file="Outputs/Fig_1b.svg", plot=Model2_data, width=7, height=4.3)

Figure 1b. b. Pocillopora spp. cover estimated using aggregated data from three datasets. The circles represent the mean values from a dataset for each month-year. The gray line represents the mean Pocillopora cover from all three datasets. The boxplots show the median (second quartile), first and third quartiles, with the bars extending from the minimum to the maximum mean coral cover recorded per dataset. Gray vertical bars demarcate the periods of “very strong” El Niño events (ONI > 2 ºC).

Model 1 (predicted values)

  • Extract model 2 predicted values
# Option 1

  # Create a new data frame for independent variables  
  NewData_1 <- expand.grid(Location=unique(aggr.location$Location),
                          Year_F=unique(aggr.location$Year_F))
  pred_1 <- predict(model1_final , newdata=NewData_1, re.form= ~(1|Location),
                    level=0)
  #summary(pred_1) 
  #length(pred_1)
  
  Predicted_Pocillopora<-cbind(NewData_1, pred_1)
  #write.csv(Predicted_Pocillopora, "Model2Predictions.c")

# Option 2
  # Effect plot
    Model1_plot<-plot(emmeans(model1_final, ~Year_F), comparisons = TRUE) +
        coord_flip(xlim = NULL, ylim = NULL, expand = TRUE) + theme_bw() +
        theme(axis.text.x = element_text(angle = 90)) + 
        ggtitle("Model 2 predictions")
 Model1_All<-grid.arrange(Model1_data, Model1_plot, ncol=2)

Aggregate data (Massives)

  • Hierarchically aggregate by location
# Aggregate by Location
  aggr.location.mas <- aggregate(Massive ~ YEAR+Month+Location, 
                        FUN=mean,data=cover)
  aggr.location.mas$Year_F<-as.factor(aggr.location.mas$YEAR)

Massives model (3)

This model includes aggregated data from Chiriqui

  • Aggregated by location
  • YEAR is a continuous variable
  • Location as a random factor

Model is NOT significant

# All years 1980_2018 
  Model3 <- lme(
    Massive ~ YEAR, random = ~1|Location, data=aggr.location.mas)
  summary(Model3)
## Linear mixed-effects model fit by REML
##   Data: aggr.location.mas 
##        AIC     BIC    logLik
##   125.6804 135.451 -58.84018
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept)  Residual
## StdDev:   0.6919983 0.4241932
## 
## Fixed effects:  Massive ~ YEAR 
##                  Value Std.Error DF     t-value p-value
## (Intercept)  0.7419698  8.531140 83  0.08697193  0.9309
## YEAR        -0.0000404  0.004263 83 -0.00948160  0.9925
##  Correlation: 
##      (Intr)
## YEAR -0.999
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -2.3877523 -0.5247623 -0.2869986  0.2727082  3.6837232 
## 
## Number of Observations: 87
## Number of Groups: 3
  anova(Model3)
  #plot(ranef(Model3))    # Symmetrical scatter effects around zero?
  #plot(Model3)           # plot residuals vs fitted
  #resnorm1 <- resid(Model3)
  #hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  #coef.m1 <- as.data.frame(coef(summary(Model3)))    # Coefficients of the model
  
  #plot(Model3, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  #plot(Model3, Massive ~ fitted(.), abline = c(0,1))

Model 3 plot (Massives, non-significant)

Massives model 4 (+ multiple comparisons between years)

This model includes data from Chiriqui * aggregated by location * Year is a factor * location as a random factor

  • Model is significant*
# All years 1980_2018 
  Model4 <- lme(
    Massive ~ -1 + Year_F, random = ~1|Location, data=aggr.location.mas)
  #summary(Model4)
  anova(Model4)
  plot(ranef(Model4))    # Symmetrical scatter effects around zero?
  plot(Model4)           # plot residuals vs fitted
  resnorm1 <- resid(Model4)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(Model4)))    # Coefficients of the model
  
  plot(Model4, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(Model4, Massive ~ fitted(.), abline = c(0,1))

  # Multicomp
    Year_F.emm<-emmeans(Model4, ~Year_F)
    #contrast(Year_F.emm, "tukey")
    year_groups<-cld(Year_F.emm, by=NULL) # compact-letter display
    year_groups<-year_groups[order(year_groups$Year_F),] 
    year_groups
    write.csv(year_groups, "Outputs/UvaNonPocilloTukey.csv", row.names = F)

Multiple comparisons among years

Summary:

  • 1980 is different from every year (1983-2018) -> Non-Pocillopora coral cover loss after 1981-82 ENSO has not recovered to pre-1982 values
  • 1994-1997 artifact differences by incorporating Uva1m2?
  • 1997 marginally different from 1998 (p=0.06)
  • 1997 different from 1999-2018 (p<0.05), except 2004-2006 -> Massive coral cover lose after 1997-98 ENSO has not recovered to pre-1997 values
m.comp_Massive <- glht(Model4, linfct = mcp(Year_F = "Tukey"))
summary(m.comp_Massive, test = univariate())
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Fit: lme.formula(fixed = Massive ~ -1 + Year_F, data = aggr.location.mas, 
##     random = ~1 | Location)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## 1983 - 1980 == 0 -1.598e+00  4.149e-01  -3.852 0.000117 ***
## 1984 - 1980 == 0 -1.711e+00  3.926e-01  -4.358 1.31e-05 ***
## 1985 - 1980 == 0 -1.712e+00  3.877e-01  -4.415 1.01e-05 ***
## 1986 - 1980 == 0 -1.685e+00  4.426e-01  -3.806 0.000141 ***
## 1987 - 1980 == 0 -1.614e+00  4.426e-01  -3.647 0.000266 ***
## 1988 - 1980 == 0 -1.651e+00  4.426e-01  -3.731 0.000191 ***
## 1989 - 1980 == 0 -1.689e+00  4.197e-01  -4.024 5.71e-05 ***
## 1990 - 1980 == 0 -1.687e+00  4.197e-01  -4.020 5.81e-05 ***
## 1992 - 1980 == 0 -1.563e+00  4.426e-01  -3.531 0.000414 ***
## 1993 - 1980 == 0 -1.374e+00  4.426e-01  -3.104 0.001911 ** 
## 1994 - 1980 == 0 -1.022e+00  4.191e-01  -2.438 0.014749 *  
## 1995 - 1980 == 0 -7.418e-01  4.191e-01  -1.770 0.076716 .  
## 1997 - 1980 == 0 -8.880e-01  3.977e-01  -2.233 0.025560 *  
## 1998 - 1980 == 0 -1.455e+00  4.439e-01  -3.277 0.001049 ** 
## 2000 - 1980 == 0 -1.441e+00  4.191e-01  -3.438 0.000585 ***
## 2001 - 1980 == 0 -1.501e+00  4.489e-01  -3.344 0.000826 ***
## 2002 - 1980 == 0 -1.402e+00  4.191e-01  -3.344 0.000825 ***
## 2003 - 1980 == 0 -1.416e+00  4.191e-01  -3.378 0.000731 ***
## 2004 - 1980 == 0 -1.104e+00  4.426e-01  -2.495 0.012604 *  
## 2005 - 1980 == 0 -1.394e+00  4.191e-01  -3.326 0.000881 ***
## 2006 - 1980 == 0 -1.257e+00  4.489e-01  -2.800 0.005104 ** 
## 2007 - 1980 == 0 -1.414e+00  4.191e-01  -3.375 0.000739 ***
## 2010 - 1980 == 0 -1.414e+00  4.191e-01  -3.374 0.000741 ***
## 2014 - 1980 == 0 -1.488e+00  4.191e-01  -3.551 0.000383 ***
## 2015 - 1980 == 0 -1.432e+00  4.191e-01  -3.417 0.000633 ***
## 2016 - 1980 == 0 -1.761e+00  4.191e-01  -4.201 2.66e-05 ***
## 2017 - 1980 == 0 -1.574e+00  4.191e-01  -3.756 0.000172 ***
## 2018 - 1980 == 0 -1.651e+00  4.191e-01  -3.940 8.15e-05 ***
## 1984 - 1983 == 0 -1.129e-01  2.609e-01  -0.433 0.665274    
## 1985 - 1983 == 0 -1.134e-01  2.534e-01  -0.448 0.654503    
## 1986 - 1983 == 0 -8.662e-02  3.314e-01  -0.261 0.793807    
## 1987 - 1983 == 0 -1.597e-02  3.314e-01  -0.048 0.961564    
## 1988 - 1983 == 0 -5.316e-02  3.314e-01  -0.160 0.872558    
## 1989 - 1983 == 0 -9.082e-02  3.001e-01  -0.303 0.762169    
## 1990 - 1983 == 0 -8.914e-02  3.001e-01  -0.297 0.766421    
## 1992 - 1983 == 0  3.527e-02  3.314e-01   0.106 0.915237    
## 1993 - 1983 == 0  2.244e-01  3.314e-01   0.677 0.498351    
## 1994 - 1983 == 0  5.762e-01  2.993e-01   1.925 0.054186 .  
## 1995 - 1983 == 0  8.563e-01  2.993e-01   2.861 0.004218 ** 
## 1997 - 1983 == 0  7.102e-01  2.685e-01   2.645 0.008168 ** 
## 1998 - 1983 == 0  1.436e-01  3.331e-01   0.431 0.666360    
## 2000 - 1983 == 0  1.571e-01  2.993e-01   0.525 0.599608    
## 2001 - 1983 == 0  9.711e-02  3.398e-01   0.286 0.775029    
## 2002 - 1983 == 0  1.966e-01  2.993e-01   0.657 0.511322    
## 2003 - 1983 == 0  1.826e-01  2.993e-01   0.610 0.541859    
## 2004 - 1983 == 0  4.939e-01  3.314e-01   1.490 0.136115    
## 2005 - 1983 == 0  2.042e-01  2.993e-01   0.682 0.495008    
## 2006 - 1983 == 0  3.411e-01  3.398e-01   1.004 0.315486    
## 2007 - 1983 == 0  1.839e-01  2.993e-01   0.615 0.538878    
## 2010 - 1983 == 0  1.841e-01  2.993e-01   0.615 0.538415    
## 2014 - 1983 == 0  1.098e-01  2.993e-01   0.367 0.713591    
## 2015 - 1983 == 0  1.661e-01  2.993e-01   0.555 0.578987    
## 2016 - 1983 == 0 -1.625e-01  2.993e-01  -0.543 0.587169    
## 2017 - 1983 == 0  2.388e-02  2.993e-01   0.080 0.936408    
## 2018 - 1983 == 0 -5.308e-02  2.993e-01  -0.177 0.859236    
## 1985 - 1984 == 0 -5.331e-04  1.862e-01  -0.003 0.997716    
## 1986 - 1984 == 0  2.625e-02  2.901e-01   0.090 0.927907    
## 1987 - 1984 == 0  9.690e-02  2.901e-01   0.334 0.738353    
## 1988 - 1984 == 0  5.971e-02  2.901e-01   0.206 0.836927    
## 1989 - 1984 == 0  2.205e-02  2.486e-01   0.089 0.929329    
## 1990 - 1984 == 0  2.372e-02  2.486e-01   0.095 0.923982    
## 1992 - 1984 == 0  1.481e-01  2.901e-01   0.511 0.609565    
## 1993 - 1984 == 0  3.373e-01  2.901e-01   1.163 0.244967    
## 1994 - 1984 == 0  6.891e-01  2.527e-01   2.727 0.006393 ** 
## 1995 - 1984 == 0  9.692e-01  2.527e-01   3.836 0.000125 ***
## 1997 - 1984 == 0  8.230e-01  2.189e-01   3.760 0.000170 ***
## 1998 - 1984 == 0  2.565e-01  2.984e-01   0.859 0.390111    
## 2000 - 1984 == 0  2.700e-01  2.527e-01   1.068 0.285344    
## 2001 - 1984 == 0  2.100e-01  2.931e-01   0.716 0.473698    
## 2002 - 1984 == 0  3.094e-01  2.527e-01   1.225 0.220761    
## 2003 - 1984 == 0  2.954e-01  2.527e-01   1.169 0.242361    
## 2004 - 1984 == 0  6.068e-01  2.901e-01   2.092 0.036449 *  
## 2005 - 1984 == 0  3.171e-01  2.527e-01   1.255 0.209549    
## 2006 - 1984 == 0  4.539e-01  2.931e-01   1.549 0.121413    
## 2007 - 1984 == 0  2.968e-01  2.527e-01   1.174 0.240218    
## 2010 - 1984 == 0  2.970e-01  2.527e-01   1.175 0.239885    
## 2014 - 1984 == 0  2.227e-01  2.527e-01   0.881 0.378128    
## 2015 - 1984 == 0  2.789e-01  2.527e-01   1.104 0.269679    
## 2016 - 1984 == 0 -4.962e-02  2.527e-01  -0.196 0.844318    
## 2017 - 1984 == 0  1.367e-01  2.527e-01   0.541 0.588405    
## 2018 - 1984 == 0  5.979e-02  2.527e-01   0.237 0.812954    
## 1986 - 1985 == 0  2.678e-02  2.851e-01   0.094 0.925155    
## 1987 - 1985 == 0  9.743e-02  2.851e-01   0.342 0.732510    
## 1988 - 1985 == 0  6.024e-02  2.851e-01   0.211 0.832637    
## 1989 - 1985 == 0  2.258e-02  2.434e-01   0.093 0.926077    
## 1990 - 1985 == 0  2.426e-02  2.434e-01   0.100 0.920618    
## 1992 - 1985 == 0  1.487e-01  2.851e-01   0.522 0.601977    
## 1993 - 1985 == 0  3.378e-01  2.851e-01   1.185 0.236014    
## 1994 - 1985 == 0  6.896e-01  2.469e-01   2.793 0.005225 ** 
## 1995 - 1985 == 0  9.697e-01  2.469e-01   3.927 8.59e-05 ***
## 1997 - 1985 == 0  8.236e-01  2.117e-01   3.890 0.000100 ***
## 1998 - 1985 == 0  2.570e-01  2.927e-01   0.878 0.379978    
## 2000 - 1985 == 0  2.705e-01  2.469e-01   1.096 0.273283    
## 2001 - 1985 == 0  2.105e-01  2.889e-01   0.729 0.466269    
## 2002 - 1985 == 0  3.100e-01  2.469e-01   1.255 0.209370    
## 2003 - 1985 == 0  2.960e-01  2.469e-01   1.199 0.230682    
## 2004 - 1985 == 0  6.073e-01  2.851e-01   2.131 0.033122 *  
## 2005 - 1985 == 0  3.176e-01  2.469e-01   1.286 0.198335    
## 2006 - 1985 == 0  4.545e-01  2.889e-01   1.573 0.115751    
## 2007 - 1985 == 0  2.973e-01  2.469e-01   1.204 0.228564    
## 2010 - 1985 == 0  2.975e-01  2.469e-01   1.205 0.228236    
## 2014 - 1985 == 0  2.232e-01  2.469e-01   0.904 0.365931    
## 2015 - 1985 == 0  2.795e-01  2.469e-01   1.132 0.257730    
## 2016 - 1985 == 0 -4.909e-02  2.469e-01  -0.199 0.842414    
## 2017 - 1985 == 0  1.373e-01  2.469e-01   0.556 0.578237    
## 2018 - 1985 == 0  6.032e-02  2.469e-01   0.244 0.806991    
## 1987 - 1986 == 0  7.065e-02  3.593e-01   0.197 0.844127    
## 1988 - 1986 == 0  3.346e-02  3.593e-01   0.093 0.925811    
## 1989 - 1986 == 0 -4.196e-03  3.284e-01  -0.013 0.989805    
## 1990 - 1986 == 0 -2.523e-03  3.284e-01  -0.008 0.993869    
## 1992 - 1986 == 0  1.219e-01  3.593e-01   0.339 0.734436    
## 1993 - 1986 == 0  3.110e-01  3.593e-01   0.866 0.386738    
## 1994 - 1986 == 0  6.628e-01  3.299e-01   2.009 0.044519 *  
## 1995 - 1986 == 0  9.430e-01  3.299e-01   2.858 0.004259 ** 
## 1997 - 1986 == 0  7.968e-01  3.037e-01   2.623 0.008706 ** 
## 1998 - 1986 == 0  2.302e-01  3.639e-01   0.633 0.526983    
## 2000 - 1986 == 0  2.437e-01  3.299e-01   0.739 0.460031    
## 2001 - 1986 == 0  1.837e-01  3.640e-01   0.505 0.613701    
## 2002 - 1986 == 0  2.832e-01  3.299e-01   0.858 0.390686    
## 2003 - 1986 == 0  2.692e-01  3.299e-01   0.816 0.414534    
## 2004 - 1986 == 0  5.806e-01  3.593e-01   1.616 0.106162    
## 2005 - 1986 == 0  2.908e-01  3.299e-01   0.882 0.378002    
## 2006 - 1986 == 0  4.277e-01  3.640e-01   1.175 0.239977    
## 2007 - 1986 == 0  2.705e-01  3.299e-01   0.820 0.412201    
## 2010 - 1986 == 0  2.707e-01  3.299e-01   0.821 0.411838    
## 2014 - 1986 == 0  1.965e-01  3.299e-01   0.596 0.551490    
## 2015 - 1986 == 0  2.527e-01  3.299e-01   0.766 0.443724    
## 2016 - 1986 == 0 -7.587e-02  3.299e-01  -0.230 0.818114    
## 2017 - 1986 == 0  1.105e-01  3.299e-01   0.335 0.737666    
## 2018 - 1986 == 0  3.355e-02  3.299e-01   0.102 0.919007    
## 1988 - 1987 == 0 -3.719e-02  3.593e-01  -0.104 0.917565    
## 1989 - 1987 == 0 -7.485e-02  3.284e-01  -0.228 0.819713    
## 1990 - 1987 == 0 -7.317e-02  3.284e-01  -0.223 0.823676    
## 1992 - 1987 == 0  5.124e-02  3.593e-01   0.143 0.886596    
## 1993 - 1987 == 0  2.404e-01  3.593e-01   0.669 0.503540    
## 1994 - 1987 == 0  5.922e-01  3.299e-01   1.795 0.072651 .  
## 1995 - 1987 == 0  8.723e-01  3.299e-01   2.644 0.008189 ** 
## 1997 - 1987 == 0  7.261e-01  3.037e-01   2.391 0.016813 *  
## 1998 - 1987 == 0  1.596e-01  3.639e-01   0.438 0.661030    
## 2000 - 1987 == 0  1.731e-01  3.299e-01   0.525 0.599834    
## 2001 - 1987 == 0  1.131e-01  3.640e-01   0.311 0.756041    
## 2002 - 1987 == 0  2.125e-01  3.299e-01   0.644 0.519434    
## 2003 - 1987 == 0  1.985e-01  3.299e-01   0.602 0.547318    
## 2004 - 1987 == 0  5.099e-01  3.593e-01   1.419 0.155878    
## 2005 - 1987 == 0  2.202e-01  3.299e-01   0.667 0.504499    
## 2006 - 1987 == 0  3.570e-01  3.640e-01   0.981 0.326627    
## 2007 - 1987 == 0  1.999e-01  3.299e-01   0.606 0.544600    
## 2010 - 1987 == 0  2.001e-01  3.299e-01   0.607 0.544177    
## 2014 - 1987 == 0  1.258e-01  3.299e-01   0.381 0.702926    
## 2015 - 1987 == 0  1.820e-01  3.299e-01   0.552 0.581110    
## 2016 - 1987 == 0 -1.465e-01  3.299e-01  -0.444 0.656951    
## 2017 - 1987 == 0  3.985e-02  3.299e-01   0.121 0.903858    
## 2018 - 1987 == 0 -3.710e-02  3.299e-01  -0.112 0.910450    
## 1989 - 1988 == 0 -3.766e-02  3.284e-01  -0.115 0.908711    
## 1990 - 1988 == 0 -3.598e-02  3.284e-01  -0.110 0.912750    
## 1992 - 1988 == 0  8.844e-02  3.593e-01   0.246 0.805594    
## 1993 - 1988 == 0  2.776e-01  3.593e-01   0.772 0.439859    
## 1994 - 1988 == 0  6.294e-01  3.299e-01   1.908 0.056424 .  
## 1995 - 1988 == 0  9.095e-01  3.299e-01   2.757 0.005835 ** 
## 1997 - 1988 == 0  7.633e-01  3.037e-01   2.513 0.011963 *  
## 1998 - 1988 == 0  1.968e-01  3.639e-01   0.541 0.588727    
## 2000 - 1988 == 0  2.103e-01  3.299e-01   0.637 0.523882    
## 2001 - 1988 == 0  1.503e-01  3.640e-01   0.413 0.679704    
## 2002 - 1988 == 0  2.497e-01  3.299e-01   0.757 0.449079    
## 2003 - 1988 == 0  2.357e-01  3.299e-01   0.715 0.474907    
## 2004 - 1988 == 0  5.471e-01  3.593e-01   1.523 0.127866    
## 2005 - 1988 == 0  2.574e-01  3.299e-01   0.780 0.435296    
## 2006 - 1988 == 0  3.942e-01  3.640e-01   1.083 0.278758    
## 2007 - 1988 == 0  2.371e-01  3.299e-01   0.719 0.472384    
## 2010 - 1988 == 0  2.373e-01  3.299e-01   0.719 0.471992    
## 2014 - 1988 == 0  1.630e-01  3.299e-01   0.494 0.621231    
## 2015 - 1988 == 0  2.192e-01  3.299e-01   0.664 0.506372    
## 2016 - 1988 == 0 -1.093e-01  3.299e-01  -0.331 0.740347    
## 2017 - 1988 == 0  7.704e-02  3.299e-01   0.234 0.815356    
## 2018 - 1988 == 0  8.651e-05  3.299e-01   0.000 0.999791    
## 1990 - 1989 == 0  1.673e-03  2.934e-01   0.006 0.995450    
## 1992 - 1989 == 0  1.261e-01  3.284e-01   0.384 0.701010    
## 1993 - 1989 == 0  3.152e-01  3.284e-01   0.960 0.337133    
## 1994 - 1989 == 0  6.670e-01  2.959e-01   2.254 0.024185 *  
## 1995 - 1989 == 0  9.472e-01  2.959e-01   3.201 0.001370 ** 
## 1997 - 1989 == 0  8.010e-01  2.670e-01   3.000 0.002697 ** 
## 1998 - 1989 == 0  2.344e-01  3.345e-01   0.701 0.483461    
## 2000 - 1989 == 0  2.479e-01  2.959e-01   0.838 0.402111    
## 2001 - 1989 == 0  1.879e-01  3.323e-01   0.565 0.571758    
## 2002 - 1989 == 0  2.874e-01  2.959e-01   0.971 0.331462    
## 2003 - 1989 == 0  2.734e-01  2.959e-01   0.924 0.355557    
## 2004 - 1989 == 0  5.848e-01  3.284e-01   1.781 0.074972 .  
## 2005 - 1989 == 0  2.950e-01  2.959e-01   0.997 0.318741    
## 2006 - 1989 == 0  4.319e-01  3.323e-01   1.299 0.193773    
## 2007 - 1989 == 0  2.747e-01  2.959e-01   0.928 0.353189    
## 2010 - 1989 == 0  2.749e-01  2.959e-01   0.929 0.352821    
## 2014 - 1989 == 0  2.007e-01  2.959e-01   0.678 0.497689    
## 2015 - 1989 == 0  2.569e-01  2.959e-01   0.868 0.385341    
## 2016 - 1989 == 0 -7.167e-02  2.959e-01  -0.242 0.808616    
## 2017 - 1989 == 0  1.147e-01  2.959e-01   0.388 0.698306    
## 2018 - 1989 == 0  3.774e-02  2.959e-01   0.128 0.898506    
## 1992 - 1990 == 0  1.244e-01  3.284e-01   0.379 0.704789    
## 1993 - 1990 == 0  3.135e-01  3.284e-01   0.955 0.339704    
## 1994 - 1990 == 0  6.654e-01  2.959e-01   2.249 0.024542 *  
## 1995 - 1990 == 0  9.455e-01  2.959e-01   3.195 0.001397 ** 
## 1997 - 1990 == 0  7.993e-01  2.670e-01   2.994 0.002753 ** 
## 1998 - 1990 == 0  2.328e-01  3.345e-01   0.696 0.486588    
## 2000 - 1990 == 0  2.463e-01  2.959e-01   0.832 0.405294    
## 2001 - 1990 == 0  1.863e-01  3.323e-01   0.560 0.575186    
## 2002 - 1990 == 0  2.857e-01  2.959e-01   0.966 0.334284    
## 2003 - 1990 == 0  2.717e-01  2.959e-01   0.918 0.358509    
## 2004 - 1990 == 0  5.831e-01  3.284e-01   1.776 0.075809 .  
## 2005 - 1990 == 0  2.934e-01  2.959e-01   0.991 0.321493    
## 2006 - 1990 == 0  4.302e-01  3.323e-01   1.294 0.195505    
## 2007 - 1990 == 0  2.731e-01  2.959e-01   0.923 0.356128    
## 2010 - 1990 == 0  2.733e-01  2.959e-01   0.923 0.355759    
## 2014 - 1990 == 0  1.990e-01  2.959e-01   0.672 0.501280    
## 2015 - 1990 == 0  2.552e-01  2.959e-01   0.862 0.388444    
## 2016 - 1990 == 0 -7.334e-02  2.959e-01  -0.248 0.804239    
## 2017 - 1990 == 0  1.130e-01  2.959e-01   0.382 0.702495    
## 2018 - 1990 == 0  3.607e-02  2.959e-01   0.122 0.902982    
## 1993 - 1992 == 0  1.891e-01  3.593e-01   0.526 0.598668    
## 1994 - 1992 == 0  5.409e-01  3.299e-01   1.640 0.101072    
## 1995 - 1992 == 0  8.211e-01  3.299e-01   2.489 0.012816 *  
## 1997 - 1992 == 0  6.749e-01  3.037e-01   2.222 0.026279 *  
## 1998 - 1992 == 0  1.083e-01  3.639e-01   0.298 0.765943    
## 2000 - 1992 == 0  1.218e-01  3.299e-01   0.369 0.711899    
## 2001 - 1992 == 0  6.183e-02  3.640e-01   0.170 0.865097    
## 2002 - 1992 == 0  1.613e-01  3.299e-01   0.489 0.624923    
## 2003 - 1992 == 0  1.473e-01  3.299e-01   0.446 0.655271    
## 2004 - 1992 == 0  4.587e-01  3.593e-01   1.276 0.201794    
## 2005 - 1992 == 0  1.689e-01  3.299e-01   0.512 0.608585    
## 2006 - 1992 == 0  3.058e-01  3.640e-01   0.840 0.400832    
## 2007 - 1992 == 0  1.486e-01  3.299e-01   0.451 0.652322    
## 2010 - 1992 == 0  1.488e-01  3.299e-01   0.451 0.651863    
## 2014 - 1992 == 0  7.457e-02  3.299e-01   0.226 0.821170    
## 2015 - 1992 == 0  1.308e-01  3.299e-01   0.396 0.691787    
## 2016 - 1992 == 0 -1.978e-01  3.299e-01  -0.599 0.548866    
## 2017 - 1992 == 0 -1.140e-02  3.299e-01  -0.035 0.972444    
## 2018 - 1992 == 0 -8.835e-02  3.299e-01  -0.268 0.788850    
## 1994 - 1993 == 0  3.518e-01  3.299e-01   1.066 0.286235    
## 1995 - 1993 == 0  6.319e-01  3.299e-01   1.916 0.055420 .  
## 1997 - 1993 == 0  4.858e-01  3.037e-01   1.599 0.109733    
## 1998 - 1993 == 0 -8.078e-02  3.639e-01  -0.222 0.824342    
## 2000 - 1993 == 0 -6.729e-02  3.299e-01  -0.204 0.838387    
## 2001 - 1993 == 0 -1.273e-01  3.640e-01  -0.350 0.726547    
## 2002 - 1993 == 0 -2.784e-02  3.299e-01  -0.084 0.932756    
## 2003 - 1993 == 0 -4.184e-02  3.299e-01  -0.127 0.899089    
## 2004 - 1993 == 0  2.695e-01  3.593e-01   0.750 0.453170    
## 2005 - 1993 == 0 -2.018e-02  3.299e-01  -0.061 0.951225    
## 2006 - 1993 == 0  1.167e-01  3.640e-01   0.321 0.748571    
## 2007 - 1993 == 0 -4.049e-02  3.299e-01  -0.123 0.902325    
## 2010 - 1993 == 0 -4.028e-02  3.299e-01  -0.122 0.902829    
## 2014 - 1993 == 0 -1.145e-01  3.299e-01  -0.347 0.728424    
## 2015 - 1993 == 0 -5.834e-02  3.299e-01  -0.177 0.859640    
## 2016 - 1993 == 0 -3.869e-01  3.299e-01  -1.173 0.240907    
## 2017 - 1993 == 0 -2.005e-01  3.299e-01  -0.608 0.543316    
## 2018 - 1993 == 0 -2.775e-01  3.299e-01  -0.841 0.400310    
## 1995 - 1994 == 0  2.801e-01  2.934e-01   0.955 0.339666    
## 1997 - 1994 == 0  1.340e-01  2.627e-01   0.510 0.610048    
## 1998 - 1994 == 0 -4.326e-01  3.293e-01  -1.314 0.189004    
## 2000 - 1994 == 0 -4.191e-01  2.934e-01  -1.428 0.153157    
## 2001 - 1994 == 0 -4.791e-01  3.293e-01  -1.455 0.145753    
## 2002 - 1994 == 0 -3.796e-01  2.934e-01  -1.294 0.195662    
## 2003 - 1994 == 0 -3.936e-01  2.934e-01  -1.342 0.179685    
## 2004 - 1994 == 0 -8.227e-02  3.299e-01  -0.249 0.803077    
## 2005 - 1994 == 0 -3.720e-01  2.934e-01  -1.268 0.204829    
## 2006 - 1994 == 0 -2.352e-01  3.293e-01  -0.714 0.475227    
## 2007 - 1994 == 0 -3.923e-01  2.934e-01  -1.337 0.181181    
## 2010 - 1994 == 0 -3.921e-01  2.934e-01  -1.336 0.181415    
## 2014 - 1994 == 0 -4.664e-01  2.934e-01  -1.590 0.111933    
## 2015 - 1994 == 0 -4.102e-01  2.934e-01  -1.398 0.162122    
## 2016 - 1994 == 0 -7.387e-01  2.934e-01  -2.518 0.011809 *  
## 2017 - 1994 == 0 -5.523e-01  2.934e-01  -1.883 0.059758 .  
## 2018 - 1994 == 0 -6.293e-01  2.934e-01  -2.145 0.031963 *  
## 1997 - 1995 == 0 -1.462e-01  2.627e-01  -0.556 0.577902    
## 1998 - 1995 == 0 -7.127e-01  3.293e-01  -2.164 0.030454 *  
## 2000 - 1995 == 0 -6.992e-01  2.934e-01  -2.383 0.017158 *  
## 2001 - 1995 == 0 -7.592e-01  3.293e-01  -2.305 0.021151 *  
## 2002 - 1995 == 0 -6.598e-01  2.934e-01  -2.249 0.024523 *  
## 2003 - 1995 == 0 -6.738e-01  2.934e-01  -2.297 0.021644 *  
## 2004 - 1995 == 0 -3.624e-01  3.299e-01  -1.099 0.271978    
## 2005 - 1995 == 0 -6.521e-01  2.934e-01  -2.223 0.026233 *  
## 2006 - 1995 == 0 -5.153e-01  3.293e-01  -1.565 0.117681    
## 2007 - 1995 == 0 -6.724e-01  2.934e-01  -2.292 0.021908 *  
## 2010 - 1995 == 0 -6.722e-01  2.934e-01  -2.291 0.021950 *  
## 2014 - 1995 == 0 -7.465e-01  2.934e-01  -2.544 0.010947 *  
## 2015 - 1995 == 0 -6.903e-01  2.934e-01  -2.353 0.018633 *  
## 2016 - 1995 == 0 -1.019e+00  2.934e-01  -3.473 0.000515 ***
## 2017 - 1995 == 0 -8.325e-01  2.934e-01  -2.837 0.004548 ** 
## 2018 - 1995 == 0 -9.094e-01  2.934e-01  -3.100 0.001937 ** 
## 1998 - 1997 == 0 -5.666e-01  3.012e-01  -1.881 0.059930 .  
## 2000 - 1997 == 0 -5.531e-01  2.627e-01  -2.105 0.035250 *  
## 2001 - 1997 == 0 -6.131e-01  3.026e-01  -2.026 0.042793 *  
## 2002 - 1997 == 0 -5.136e-01  2.627e-01  -1.955 0.050548 .  
## 2003 - 1997 == 0 -5.276e-01  2.627e-01  -2.009 0.044580 *  
## 2004 - 1997 == 0 -2.162e-01  3.037e-01  -0.712 0.476505    
## 2005 - 1997 == 0 -5.060e-01  2.627e-01  -1.926 0.054086 .  
## 2006 - 1997 == 0 -3.691e-01  3.026e-01  -1.220 0.222592    
## 2007 - 1997 == 0 -5.263e-01  2.627e-01  -2.003 0.045128 *  
## 2010 - 1997 == 0 -5.261e-01  2.627e-01  -2.003 0.045214 *  
## 2014 - 1997 == 0 -6.003e-01  2.627e-01  -2.285 0.022289 *  
## 2015 - 1997 == 0 -5.441e-01  2.627e-01  -2.071 0.038320 *  
## 2016 - 1997 == 0 -8.727e-01  2.627e-01  -3.322 0.000893 ***
## 2017 - 1997 == 0 -6.863e-01  2.627e-01  -2.613 0.008984 ** 
## 2018 - 1997 == 0 -7.633e-01  2.627e-01  -2.906 0.003665 ** 
## 2000 - 1998 == 0  1.350e-02  3.293e-01   0.041 0.967314    
## 2001 - 1998 == 0 -4.651e-02  3.624e-01  -0.128 0.897898    
## 2002 - 1998 == 0  5.294e-02  3.293e-01   0.161 0.872281    
## 2003 - 1998 == 0  3.895e-02  3.293e-01   0.118 0.905866    
## 2004 - 1998 == 0  3.503e-01  3.639e-01   0.963 0.335748    
## 2005 - 1998 == 0  6.060e-02  3.293e-01   0.184 0.854005    
## 2006 - 1998 == 0  1.974e-01  3.624e-01   0.545 0.585909    
## 2007 - 1998 == 0  4.029e-02  3.293e-01   0.122 0.902623    
## 2010 - 1998 == 0  4.050e-02  3.293e-01   0.123 0.902117    
## 2014 - 1998 == 0 -3.377e-02  3.293e-01  -0.103 0.918333    
## 2015 - 1998 == 0  2.244e-02  3.293e-01   0.068 0.945668    
## 2016 - 1998 == 0 -3.061e-01  3.293e-01  -0.929 0.352655    
## 2017 - 1998 == 0 -1.197e-01  3.293e-01  -0.364 0.716183    
## 2018 - 1998 == 0 -1.967e-01  3.293e-01  -0.597 0.550356    
## 2001 - 2000 == 0 -6.000e-02  3.293e-01  -0.182 0.855439    
## 2002 - 2000 == 0  3.945e-02  2.934e-01   0.134 0.893039    
## 2003 - 2000 == 0  2.545e-02  2.934e-01   0.087 0.930874    
## 2004 - 2000 == 0  3.368e-01  3.299e-01   1.021 0.307251    
## 2005 - 2000 == 0  4.711e-02  2.934e-01   0.161 0.872442    
## 2006 - 2000 == 0  1.839e-01  3.293e-01   0.559 0.576492    
## 2007 - 2000 == 0  2.680e-02  2.934e-01   0.091 0.927222    
## 2010 - 2000 == 0  2.701e-02  2.934e-01   0.092 0.926653    
## 2014 - 2000 == 0 -4.726e-02  2.934e-01  -0.161 0.872018    
## 2015 - 2000 == 0  8.948e-03  2.934e-01   0.030 0.975669    
## 2016 - 2000 == 0 -3.196e-01  2.934e-01  -1.089 0.276009    
## 2017 - 2000 == 0 -1.332e-01  2.934e-01  -0.454 0.649751    
## 2018 - 2000 == 0 -2.102e-01  2.934e-01  -0.716 0.473746    
## 2002 - 2001 == 0  9.945e-02  3.293e-01   0.302 0.762680    
## 2003 - 2001 == 0  8.545e-02  3.293e-01   0.259 0.795283    
## 2004 - 2001 == 0  3.968e-01  3.640e-01   1.090 0.275579    
## 2005 - 2001 == 0  1.071e-01  3.293e-01   0.325 0.745021    
## 2006 - 2001 == 0  2.439e-01  3.593e-01   0.679 0.497203    
## 2007 - 2001 == 0  8.680e-02  3.293e-01   0.264 0.792126    
## 2010 - 2001 == 0  8.701e-02  3.293e-01   0.264 0.791634    
## 2014 - 2001 == 0  1.274e-02  3.293e-01   0.039 0.969150    
## 2015 - 2001 == 0  6.895e-02  3.293e-01   0.209 0.834173    
## 2016 - 2001 == 0 -2.596e-01  3.293e-01  -0.788 0.430569    
## 2017 - 2001 == 0 -7.323e-02  3.293e-01  -0.222 0.824043    
## 2018 - 2001 == 0 -1.502e-01  3.293e-01  -0.456 0.648388    
## 2003 - 2002 == 0 -1.400e-02  2.934e-01  -0.048 0.961943    
## 2004 - 2002 == 0  2.974e-01  3.299e-01   0.901 0.367360    
## 2005 - 2002 == 0  7.657e-03  2.934e-01   0.026 0.979180    
## 2006 - 2002 == 0  1.445e-01  3.293e-01   0.439 0.660853    
## 2007 - 2002 == 0 -1.265e-02  2.934e-01  -0.043 0.965607    
## 2010 - 2002 == 0 -1.244e-02  2.934e-01  -0.042 0.966177    
## 2014 - 2002 == 0 -8.671e-02  2.934e-01  -0.296 0.767570    
## 2015 - 2002 == 0 -3.050e-02  2.934e-01  -0.104 0.917201    
## 2016 - 2002 == 0 -3.590e-01  2.934e-01  -1.224 0.221032    
## 2017 - 2002 == 0 -1.727e-01  2.934e-01  -0.589 0.556151    
## 2018 - 2002 == 0 -2.496e-01  2.934e-01  -0.851 0.394848    
## 2004 - 2003 == 0  3.114e-01  3.299e-01   0.944 0.345240    
## 2005 - 2003 == 0  2.166e-02  2.934e-01   0.074 0.941160    
## 2006 - 2003 == 0  1.585e-01  3.293e-01   0.481 0.630344    
## 2007 - 2003 == 0  1.348e-03  2.934e-01   0.005 0.996333    
## 2010 - 2003 == 0  1.558e-03  2.934e-01   0.005 0.995762    
## 2014 - 2003 == 0 -7.271e-02  2.934e-01  -0.248 0.804258    
## 2015 - 2003 == 0 -1.650e-02  2.934e-01  -0.056 0.955146    
## 2016 - 2003 == 0 -3.450e-01  2.934e-01  -1.176 0.239566    
## 2017 - 2003 == 0 -1.587e-01  2.934e-01  -0.541 0.588609    
## 2018 - 2003 == 0 -2.356e-01  2.934e-01  -0.803 0.421892    
## 2005 - 2004 == 0 -2.897e-01  3.299e-01  -0.878 0.379824    
## 2006 - 2004 == 0 -1.529e-01  3.640e-01  -0.420 0.674443    
## 2007 - 2004 == 0 -3.100e-01  3.299e-01  -0.940 0.347333    
## 2010 - 2004 == 0 -3.098e-01  3.299e-01  -0.939 0.347659    
## 2014 - 2004 == 0 -3.841e-01  3.299e-01  -1.164 0.244313    
## 2015 - 2004 == 0 -3.279e-01  3.299e-01  -0.994 0.320280    
## 2016 - 2004 == 0 -6.564e-01  3.299e-01  -1.990 0.046616 *  
## 2017 - 2004 == 0 -4.701e-01  3.299e-01  -1.425 0.154198    
## 2018 - 2004 == 0 -5.470e-01  3.299e-01  -1.658 0.097294 .  
## 2006 - 2005 == 0  1.368e-01  3.293e-01   0.415 0.677785    
## 2007 - 2005 == 0 -2.031e-02  2.934e-01  -0.069 0.944817    
## 2010 - 2005 == 0 -2.010e-02  2.934e-01  -0.069 0.945387    
## 2014 - 2005 == 0 -9.437e-02  2.934e-01  -0.322 0.747716    
## 2015 - 2005 == 0 -3.816e-02  2.934e-01  -0.130 0.896520    
## 2016 - 2005 == 0 -3.667e-01  2.934e-01  -1.250 0.211342    
## 2017 - 2005 == 0 -1.803e-01  2.934e-01  -0.615 0.538775    
## 2018 - 2005 == 0 -2.573e-01  2.934e-01  -0.877 0.380511    
## 2007 - 2006 == 0 -1.571e-01  3.293e-01  -0.477 0.633257    
## 2010 - 2006 == 0 -1.569e-01  3.293e-01  -0.477 0.633711    
## 2014 - 2006 == 0 -2.312e-01  3.293e-01  -0.702 0.482664    
## 2015 - 2006 == 0 -1.750e-01  3.293e-01  -0.531 0.595178    
## 2016 - 2006 == 0 -5.035e-01  3.293e-01  -1.529 0.126285    
## 2017 - 2006 == 0 -3.172e-01  3.293e-01  -0.963 0.335524    
## 2018 - 2006 == 0 -3.941e-01  3.293e-01  -1.197 0.231423    
## 2010 - 2007 == 0  2.101e-04  2.934e-01   0.001 0.999429    
## 2014 - 2007 == 0 -7.406e-02  2.934e-01  -0.252 0.800704    
## 2015 - 2007 == 0 -1.785e-02  2.934e-01  -0.061 0.951485    
## 2016 - 2007 == 0 -3.464e-01  2.934e-01  -1.181 0.237734    
## 2017 - 2007 == 0 -1.600e-01  2.934e-01  -0.545 0.585445    
## 2018 - 2007 == 0 -2.370e-01  2.934e-01  -0.808 0.419241    
## 2014 - 2010 == 0 -7.427e-02  2.934e-01  -0.253 0.800151    
## 2015 - 2010 == 0 -1.806e-02  2.934e-01  -0.062 0.950915    
## 2016 - 2010 == 0 -3.466e-01  2.934e-01  -1.181 0.237450    
## 2017 - 2010 == 0 -1.602e-01  2.934e-01  -0.546 0.584952    
## 2018 - 2010 == 0 -2.372e-01  2.934e-01  -0.808 0.418829    
## 2015 - 2014 == 0  5.621e-02  2.934e-01   0.192 0.848060    
## 2016 - 2014 == 0 -2.723e-01  2.934e-01  -0.928 0.353287    
## 2017 - 2014 == 0 -8.597e-02  2.934e-01  -0.293 0.769512    
## 2018 - 2014 == 0 -1.629e-01  2.934e-01  -0.555 0.578688    
## 2016 - 2015 == 0 -3.285e-01  2.934e-01  -1.120 0.262788    
## 2017 - 2015 == 0 -1.422e-01  2.934e-01  -0.485 0.627955    
## 2018 - 2015 == 0 -2.191e-01  2.934e-01  -0.747 0.455126    
## 2017 - 2016 == 0  1.864e-01  2.934e-01   0.635 0.525286    
## 2018 - 2016 == 0  1.094e-01  2.934e-01   0.373 0.709201    
## 2018 - 2017 == 0 -7.695e-02  2.934e-01  -0.262 0.793098    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

Model 4 plot (Massives, significant)

 Model4_All<-grid.arrange(massives_plot, model4_plot, ncol=2)

Aggregate data (Millepora)

  • Hierarchically aggregate by location
# Aggregate by Location
  aggr.location.mill <- aggregate(Millepora ~ YEAR+Month+Location, 
                        FUN=mean,data=cover)
  aggr.location.mill$Year_F<-as.factor(aggr.location.mill$YEAR)

Millepora model (5)

This model includes aggregated data from Chiriqui

  • Aggregated by location
  • YEAR is continuous
  • Location as a random factor

Model is NOT significant

# All years 1980_2018 
  Model5 <- lme(Millepora ~ YEAR, random = ~1|Location, data=aggr.location.mill)
  summary(Model5)
## Linear mixed-effects model fit by REML
##   Data: aggr.location.mill 
##        AIC      BIC    logLik
##   377.6839 387.4545 -184.8419
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    1.036569 1.914402
## 
## Fixed effects:  Millepora ~ YEAR 
##                Value Std.Error DF   t-value p-value
## (Intercept) 57.58958  38.17441 83  1.508591  0.1352
## YEAR        -0.02853   0.01909 83 -1.494158  0.1389
##  Correlation: 
##      (Intr)
## YEAR -1    
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -0.88787712 -0.19988893 -0.11320291  0.09071803  6.59088878 
## 
## Number of Observations: 87
## Number of Groups: 3
  anova(Model5)
  #plot(ranef(Model5))    # Symmetrical scatter effects around zero?
  #plot(Model5)           # plot residuals vs fitted
  #resnorm1 <- resid(Model5)
  #hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  #coef.m1 <- as.data.frame(coef(summary(Model5)))    # Coefficients of the model
  
  #plot(Model5, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  #plot(Model5, Millepora ~ fitted(.), abline = c(0,1))

Millepora model 6 (multiple comparisons between years)

This model includes data from Chiriqui * aggregated by location * Year is a factor * location as a random factor

# All years 1980_2018 
  Model6 <- lme(
    Millepora ~ -1 + Year_F, random = ~1|Location, data=aggr.location.mill)
  #summary(Model6)
  anova(Model6)

Millepora plots (non-significant models)

Aggregate data (all Scleractinians)

  • Hierarchically aggregate by location
# Aggregate by Location
  aggr.location.scl <- aggregate(All_Corals ~ YEAR+Month+Location, 
                        FUN=mean,data=cover)
  aggr.location.scl$Year_F<-as.factor(aggr.location.scl$YEAR)

All scleractinians (model 7)

This model includes aggregated data from Chiriqui

  • Aggregated by location
  • YEAR as a continuous variable
  • Location as a random factor

Model is significant

# All years 1980_2018 
  Model7 <- lme(All_Corals ~ YEAR, random = ~1|Location, data=aggr.location.scl)
  summary(Model7)
## Linear mixed-effects model fit by REML
##   Data: aggr.location.scl 
##        AIC     BIC    logLik
##   727.2946 737.112 -359.6473
## 
## Random effects:
##  Formula: ~1 | Location
##         (Intercept) Residual
## StdDev:    9.033042   14.216
## 
## Fixed effects:  All_Corals ~ YEAR 
##                  Value Std.Error DF   t-value p-value
## (Intercept) -3018.5300 280.78547 84 -10.75031       0
## YEAR            1.5216   0.14045 84  10.83406       0
##  Correlation: 
##      (Intr)
## YEAR -1    
## 
## Standardized Within-Group Residuals:
##        Min         Q1        Med         Q3        Max 
## -1.1579451 -0.6162544 -0.2954427  0.4970609  5.2973659 
## 
## Number of Observations: 88
## Number of Groups: 3
  anova(Model7)
  plot(ranef(Model7))    # Symmetrical scatter effects around zero?
  plot(Model7)           # plot residuals vs fitted
  resnorm1 <- resid(Model7)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(Model7)))    # Coefficients of the model
  
  plot(Model7, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(Model7, All_Corals ~ fitted(.), abline = c(0,1))

Model 7 plot

Scleractinian_plot <- ggplot(aggr.location.scl, 
                             aes(x=YEAR, y=All_Corals)) +
  #geom_boxplot(aes(group=YEAR), outlier.shape = NA) +
  #stat_boxplot(aes(group=YEAR), geom = 'errorbar')+
  geom_point(aes(fill=factor(Location)),
                 shape = 21, colour = "black",
                 size = 2, stroke = 0.8, alpha=0.5) +
  geom_smooth(method = lm, se=FALSE, linetype = "dashed", colour="red")+
  geom_smooth(span = 0.3, se=T, colour="darkgray")+ 
  scale_y_continuous("Coral cover (%)", limits = c(-0.5, 80), expand = c(0,0))+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1979, 2019, by=2), expand = c(0,0))+
  annotate("rect", xmin = 1982, xmax = 1983, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 1997, xmax = 1998, 
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 2015, xmax = 2016,
           ymin = 0, ymax = 80,  alpha = .2, fill="gray")

Scleractinian_plot + theme(legend.position = c(0.25, 0.8))

Scleractinians model 8 (multiple comparisons between years)

This model includes data from Chiriqui

  • Aggregated by location
  • Year as a factor
  • Location as a random factor
# All years 1980_2018 
  Model8 <- lme(
    All_Corals ~ -1 + Year_F, random = ~1|Location, data=aggr.location.scl)
  #summary(Model8)
  anova(Model8)
  plot(ranef(Model8))    # Symmetrical scatter effects around zero?
  plot(Model8)           # plot residuals vs fitted
  resnorm1 <- resid(Model8)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(Model8)))    # Coefficients of the model
  
  plot(Model8, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(Model8, All_Corals ~ fitted(.), abline = c(0,1))
  
  # Multicomp
    Year_F.emm_scle<-emmeans(Model8, ~Year_F)
    #contrast(Year_F.emm, "tukey")
    year_groups_Scle<-cld(Year_F.emm_scle, by=NULL) # compact-letter display
    year_groups_Scle

Model 8 plot data

Model 8 plot

# Effect plot
  Model8_predictoin<-plot(emmeans(Model8, ~Year_F), comparisons = TRUE) +
      coord_flip(xlim = NULL, ylim = NULL, expand = TRUE) + theme_bw()+
    theme(axis.text.x = element_text(angle = 90)) + 
    ggtitle("Model 8 predictions (All scleractinians)")
 Model8_All<-grid.arrange(Scleractinian_plot, Model8_predictoin, ncol=2)

Summary:

  • Pretty much the same as only Pocillopora …

  • 1980 is different from 1983-2001 -> Coral cover lose after 1981-82 ENSO
  • “Recovery” by 2002 (no differences between 1980 and 2002) uninterrupted until 2018 -> no significant cover loss in 1997-98 nor 2015-16
  • 1997 not different from 1998, 2000, 2001, 2003
  • 2015 not different from 2016, 2017, 2018

m.comp_sclera <- glht(Model8, linfct = mcp(Year_F = "Tukey"))
summary(m.comp_sclera, test = univariate())
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Multiple Comparisons of Means: Tukey Contrasts
## 
## 
## Fit: lme.formula(fixed = All_Corals ~ -1 + Year_F, data = aggr.location.scl, 
##     random = ~1 | Location)
## 
## Linear Hypotheses:
##                  Estimate Std. Error z value Pr(>|z|)    
## 1983 - 1980 == 0 -28.6380    10.8980  -2.628 0.008593 ** 
## 1984 - 1980 == 0 -52.3502     9.5407  -5.487 4.09e-08 ***
## 1985 - 1980 == 0 -49.9089     9.3775  -5.322 1.03e-07 ***
## 1986 - 1980 == 0 -44.5140    11.8233  -3.765 0.000167 ***
## 1987 - 1980 == 0 -44.1940    11.8233  -3.738 0.000186 ***
## 1988 - 1980 == 0 -43.2755    11.8233  -3.660 0.000252 ***
## 1989 - 1980 == 0 -47.6223    10.8048  -4.408 1.05e-05 ***
## 1990 - 1980 == 0 -46.4883    10.8048  -4.303 1.69e-05 ***
## 1992 - 1980 == 0 -41.2590    11.8233  -3.490 0.000484 ***
## 1993 - 1980 == 0 -40.3945    11.8233  -3.417 0.000634 ***
## 1994 - 1980 == 0 -39.9292    10.8521  -3.679 0.000234 ***
## 1995 - 1980 == 0 -31.0275    10.8521  -2.859 0.004248 ** 
## 1997 - 1980 == 0 -28.4906     9.9890  -2.852 0.004342 ** 
## 1998 - 1980 == 0 -30.6310    11.9675  -2.560 0.010482 *  
## 2000 - 1980 == 0 -26.1579    10.8521  -2.410 0.015935 *  
## 2001 - 1980 == 0 -25.4153    11.9683  -2.124 0.033708 *  
## 2002 - 1980 == 0 -16.7682    10.8521  -1.545 0.122309    
## 2003 - 1980 == 0 -14.4000    10.8521  -1.327 0.184532    
## 2004 - 1980 == 0  -8.6560    11.8233  -0.732 0.464099    
## 2005 - 1980 == 0 -10.8151    10.8521  -0.997 0.318965    
## 2006 - 1980 == 0  -2.2793    11.9683  -0.190 0.848958    
## 2007 - 1980 == 0  -7.4482    10.8521  -0.686 0.492499    
## 2010 - 1980 == 0  -2.4605    10.8521  -0.227 0.820636    
## 2014 - 1980 == 0   0.5400    10.8521   0.050 0.960310    
## 2015 - 1980 == 0   1.9508    10.8521   0.180 0.857339    
## 2016 - 1980 == 0  -6.1193    10.8521  -0.564 0.572835    
## 2017 - 1980 == 0   8.8441    10.8521   0.815 0.415091    
## 2018 - 1980 == 0  10.3253    10.8521   0.951 0.341372    
## 1984 - 1983 == 0 -23.7122     8.5587  -2.771 0.005596 ** 
## 1985 - 1983 == 0 -21.2709     8.3179  -2.557 0.010551 *  
## 1986 - 1983 == 0 -15.8760    10.8980  -1.457 0.145176    
## 1987 - 1983 == 0 -15.5560    10.8980  -1.427 0.153459    
## 1988 - 1983 == 0 -14.6375    10.8980  -1.343 0.179227    
## 1989 - 1983 == 0 -18.9844     9.8609  -1.925 0.054202 .  
## 1990 - 1983 == 0 -17.8504     9.8609  -1.810 0.070261 .  
## 1992 - 1983 == 0 -12.6210    10.8980  -1.158 0.246821    
## 1993 - 1983 == 0 -11.7565    10.8980  -1.079 0.280686    
## 1994 - 1983 == 0 -11.2912     9.8365  -1.148 0.251013    
## 1995 - 1983 == 0  -2.3895     9.8365  -0.243 0.808065    
## 1997 - 1983 == 0   0.1474     8.8239   0.017 0.986676    
## 1998 - 1983 == 0  -1.9930    10.9518  -0.182 0.855597    
## 2000 - 1983 == 0   2.4801     9.8365   0.252 0.800939    
## 2001 - 1983 == 0   3.2227    11.1584   0.289 0.772721    
## 2002 - 1983 == 0  11.8698     9.8365   1.207 0.227544    
## 2003 - 1983 == 0  14.2380     9.8365   1.447 0.147766    
## 2004 - 1983 == 0  19.9820    10.8980   1.834 0.066721 .  
## 2005 - 1983 == 0  17.8229     9.8365   1.812 0.069999 .  
## 2006 - 1983 == 0  26.3586    11.1584   2.362 0.018165 *  
## 2007 - 1983 == 0  21.1898     9.8365   2.154 0.031225 *  
## 2010 - 1983 == 0  26.1775     9.8365   2.661 0.007785 ** 
## 2014 - 1983 == 0  29.1780     9.8365   2.966 0.003014 ** 
## 2015 - 1983 == 0  30.5888     9.8365   3.110 0.001873 ** 
## 2016 - 1983 == 0  22.5187     9.8365   2.289 0.022062 *  
## 2017 - 1983 == 0  37.4821     9.8365   3.811 0.000139 ***
## 2018 - 1983 == 0  38.9633     9.8365   3.961 7.46e-05 ***
## 1985 - 1984 == 0   2.4413     6.1277   0.398 0.690334    
## 1986 - 1984 == 0   7.8362     9.5407   0.821 0.411454    
## 1987 - 1984 == 0   8.1562     9.5407   0.855 0.392619    
## 1988 - 1984 == 0   9.0747     9.5407   0.951 0.341529    
## 1989 - 1984 == 0   4.7278     8.1790   0.578 0.563237    
## 1990 - 1984 == 0   5.8618     8.1790   0.717 0.473567    
## 1992 - 1984 == 0  11.0912     9.5407   1.163 0.245030    
## 1993 - 1984 == 0  11.9557     9.5407   1.253 0.210163    
## 1994 - 1984 == 0  12.4209     8.3063   1.495 0.134820    
## 1995 - 1984 == 0  21.3227     8.3063   2.567 0.010257 *  
## 1997 - 1984 == 0  23.8595     7.1871   3.320 0.000901 ***
## 1998 - 1984 == 0  21.7191     9.8014   2.216 0.026697 *  
## 2000 - 1984 == 0  26.1923     8.3063   3.153 0.001614 ** 
## 2001 - 1984 == 0  26.9349     9.6352   2.795 0.005183 ** 
## 2002 - 1984 == 0  35.5820     8.3063   4.284 1.84e-05 ***
## 2003 - 1984 == 0  37.9502     8.3063   4.569 4.90e-06 ***
## 2004 - 1984 == 0  43.6942     9.5407   4.580 4.66e-06 ***
## 2005 - 1984 == 0  41.5351     8.3063   5.000 5.72e-07 ***
## 2006 - 1984 == 0  50.0708     9.6352   5.197 2.03e-07 ***
## 2007 - 1984 == 0  44.9019     8.3063   5.406 6.45e-08 ***
## 2010 - 1984 == 0  49.8897     8.3063   6.006 1.90e-09 ***
## 2014 - 1984 == 0  52.8902     8.3063   6.367 1.92e-10 ***
## 2015 - 1984 == 0  54.3010     8.3063   6.537 6.26e-11 ***
## 2016 - 1984 == 0  46.2308     8.3063   5.566 2.61e-08 ***
## 2017 - 1984 == 0  61.1943     8.3063   7.367 1.74e-13 ***
## 2018 - 1984 == 0  62.6755     8.3063   7.546 4.51e-14 ***
## 1986 - 1985 == 0   5.3949     9.3775   0.575 0.565088    
## 1987 - 1985 == 0   5.7149     9.3775   0.609 0.542243    
## 1988 - 1985 == 0   6.6334     9.3775   0.707 0.479335    
## 1989 - 1985 == 0   2.2865     8.0083   0.286 0.775246    
## 1990 - 1985 == 0   3.4205     8.0083   0.427 0.669290    
## 1992 - 1985 == 0   8.6499     9.3775   0.922 0.356315    
## 1993 - 1985 == 0   9.5144     9.3775   1.015 0.310298    
## 1994 - 1985 == 0   9.9797     8.1185   1.229 0.218976    
## 1995 - 1985 == 0  18.8814     8.1185   2.326 0.020033 *  
## 1997 - 1985 == 0  21.4182     6.9551   3.079 0.002074 ** 
## 1998 - 1985 == 0  19.2779     9.6175   2.004 0.045022 *  
## 2000 - 1985 == 0  23.7510     8.1185   2.926 0.003438 ** 
## 2001 - 1985 == 0  24.4936     9.4995   2.578 0.009926 ** 
## 2002 - 1985 == 0  33.1407     8.1185   4.082 4.46e-05 ***
## 2003 - 1985 == 0  35.5089     8.1185   4.374 1.22e-05 ***
## 2004 - 1985 == 0  41.2529     9.3775   4.399 1.09e-05 ***
## 2005 - 1985 == 0  39.0938     8.1185   4.815 1.47e-06 ***
## 2006 - 1985 == 0  47.6295     9.4995   5.014 5.33e-07 ***
## 2007 - 1985 == 0  42.4607     8.1185   5.230 1.69e-07 ***
## 2010 - 1985 == 0  47.4484     8.1185   5.845 5.08e-09 ***
## 2014 - 1985 == 0  50.4489     8.1185   6.214 5.16e-10 ***
## 2015 - 1985 == 0  51.8597     8.1185   6.388 1.68e-10 ***
## 2016 - 1985 == 0  43.7896     8.1185   5.394 6.90e-08 ***
## 2017 - 1985 == 0  58.7530     8.1185   7.237 4.59e-13 ***
## 2018 - 1985 == 0  60.2342     8.1185   7.419 1.18e-13 ***
## 1987 - 1986 == 0   0.3200    11.8233   0.027 0.978408    
## 1988 - 1986 == 0   1.2385    11.8233   0.105 0.916573    
## 1989 - 1986 == 0  -3.1083    10.8048  -0.288 0.773591    
## 1990 - 1986 == 0  -1.9743    10.8048  -0.183 0.855012    
## 1992 - 1986 == 0   3.2550    11.8233   0.275 0.783083    
## 1993 - 1986 == 0   4.1195    11.8233   0.348 0.727523    
## 1994 - 1986 == 0   4.5848    10.8521   0.422 0.672676    
## 1995 - 1986 == 0  13.4865    10.8521   1.243 0.213959    
## 1997 - 1986 == 0  16.0234     9.9890   1.604 0.108690    
## 1998 - 1986 == 0  13.8830    11.9675   1.160 0.246026    
## 2000 - 1986 == 0  18.3561    10.8521   1.691 0.090746 .  
## 2001 - 1986 == 0  19.0987    11.9683   1.596 0.110539    
## 2002 - 1986 == 0  27.7458    10.8521   2.557 0.010566 *  
## 2003 - 1986 == 0  30.1140    10.8521   2.775 0.005521 ** 
## 2004 - 1986 == 0  35.8580    11.8233   3.033 0.002423 ** 
## 2005 - 1986 == 0  33.6989    10.8521   3.105 0.001901 ** 
## 2006 - 1986 == 0  42.2347    11.9683   3.529 0.000417 ***
## 2007 - 1986 == 0  37.0658    10.8521   3.416 0.000637 ***
## 2010 - 1986 == 0  42.0535    10.8521   3.875 0.000107 ***
## 2014 - 1986 == 0  45.0540    10.8521   4.152 3.30e-05 ***
## 2015 - 1986 == 0  46.4648    10.8521   4.282 1.86e-05 ***
## 2016 - 1986 == 0  38.3947    10.8521   3.538 0.000403 ***
## 2017 - 1986 == 0  53.3581    10.8521   4.917 8.80e-07 ***
## 2018 - 1986 == 0  54.8393    10.8521   5.053 4.34e-07 ***
## 1988 - 1987 == 0   0.9185    11.8233   0.078 0.938078    
## 1989 - 1987 == 0  -3.4283    10.8048  -0.317 0.751019    
## 1990 - 1987 == 0  -2.2943    10.8048  -0.212 0.831839    
## 1992 - 1987 == 0   2.9350    11.8233   0.248 0.803950    
## 1993 - 1987 == 0   3.7995    11.8233   0.321 0.747940    
## 1994 - 1987 == 0   4.2648    10.8521   0.393 0.694327    
## 1995 - 1987 == 0  13.1665    10.8521   1.213 0.225028    
## 1997 - 1987 == 0  15.7034     9.9890   1.572 0.115934    
## 1998 - 1987 == 0  13.5630    11.9675   1.133 0.257082    
## 2000 - 1987 == 0  18.0361    10.8521   1.662 0.096515 .  
## 2001 - 1987 == 0  18.7787    11.9683   1.569 0.116639    
## 2002 - 1987 == 0  27.4258    10.8521   2.527 0.011497 *  
## 2003 - 1987 == 0  29.7940    10.8521   2.745 0.006043 ** 
## 2004 - 1987 == 0  35.5380    11.8233   3.006 0.002649 ** 
## 2005 - 1987 == 0  33.3789    10.8521   3.076 0.002099 ** 
## 2006 - 1987 == 0  41.9147    11.9683   3.502 0.000462 ***
## 2007 - 1987 == 0  36.7458    10.8521   3.386 0.000709 ***
## 2010 - 1987 == 0  41.7335    10.8521   3.846 0.000120 ***
## 2014 - 1987 == 0  44.7340    10.8521   4.122 3.75e-05 ***
## 2015 - 1987 == 0  46.1448    10.8521   4.252 2.12e-05 ***
## 2016 - 1987 == 0  38.0747    10.8521   3.509 0.000451 ***
## 2017 - 1987 == 0  53.0381    10.8521   4.887 1.02e-06 ***
## 2018 - 1987 == 0  54.5193    10.8521   5.024 5.06e-07 ***
## 1989 - 1988 == 0  -4.3468    10.8048  -0.402 0.687460    
## 1990 - 1988 == 0  -3.2128    10.8048  -0.297 0.766198    
## 1992 - 1988 == 0   2.0165    11.8233   0.171 0.864575    
## 1993 - 1988 == 0   2.8810    11.8233   0.244 0.807485    
## 1994 - 1988 == 0   3.3463    10.8521   0.308 0.757814    
## 1995 - 1988 == 0  12.2480    10.8521   1.129 0.259055    
## 1997 - 1988 == 0  14.7849     9.9890   1.480 0.138841    
## 1998 - 1988 == 0  12.6445    11.9675   1.057 0.290709    
## 2000 - 1988 == 0  17.1176    10.8521   1.577 0.114714    
## 2001 - 1988 == 0  17.8602    11.9683   1.492 0.135622    
## 2002 - 1988 == 0  26.5073    10.8521   2.443 0.014582 *  
## 2003 - 1988 == 0  28.8755    10.8521   2.661 0.007795 ** 
## 2004 - 1988 == 0  34.6195    11.8233   2.928 0.003411 ** 
## 2005 - 1988 == 0  32.4604    10.8521   2.991 0.002779 ** 
## 2006 - 1988 == 0  40.9962    11.9683   3.425 0.000614 ***
## 2007 - 1988 == 0  35.8273    10.8521   3.301 0.000962 ***
## 2010 - 1988 == 0  40.8150    10.8521   3.761 0.000169 ***
## 2014 - 1988 == 0  43.8155    10.8521   4.038 5.40e-05 ***
## 2015 - 1988 == 0  45.2263    10.8521   4.168 3.08e-05 ***
## 2016 - 1988 == 0  37.1562    10.8521   3.424 0.000617 ***
## 2017 - 1988 == 0  52.1196    10.8521   4.803 1.57e-06 ***
## 2018 - 1988 == 0  53.6008    10.8521   4.939 7.84e-07 ***
## 1990 - 1989 == 0   1.1340     9.6537   0.117 0.906489    
## 1992 - 1989 == 0   6.3633    10.8048   0.589 0.555905    
## 1993 - 1989 == 0   7.2278    10.8048   0.669 0.503531    
## 1994 - 1989 == 0   7.6931     9.7323   0.790 0.429254    
## 1995 - 1989 == 0  16.5948     9.7323   1.705 0.088172 .  
## 1997 - 1989 == 0  19.1317     8.7768   2.180 0.029272 *  
## 1998 - 1989 == 0  16.9913    10.9967   1.545 0.122316    
## 2000 - 1989 == 0  21.4644     9.7323   2.205 0.027421 *  
## 2001 - 1989 == 0  22.2071    10.9284   2.032 0.042149 *  
## 2002 - 1989 == 0  30.8541     9.7323   3.170 0.001523 ** 
## 2003 - 1989 == 0  33.2224     9.7323   3.414 0.000641 ***
## 2004 - 1989 == 0  38.9663    10.8048   3.606 0.000310 ***
## 2005 - 1989 == 0  36.8073     9.7323   3.782 0.000156 ***
## 2006 - 1989 == 0  45.3430    10.9284   4.149 3.34e-05 ***
## 2007 - 1989 == 0  40.1741     9.7323   4.128 3.66e-05 ***
## 2010 - 1989 == 0  45.1619     9.7323   4.640 3.48e-06 ***
## 2014 - 1989 == 0  48.1624     9.7323   4.949 7.47e-07 ***
## 2015 - 1989 == 0  49.5731     9.7323   5.094 3.51e-07 ***
## 2016 - 1989 == 0  41.5030     9.7323   4.264 2.00e-05 ***
## 2017 - 1989 == 0  56.4664     9.7323   5.802 6.56e-09 ***
## 2018 - 1989 == 0  57.9477     9.7323   5.954 2.61e-09 ***
## 1992 - 1990 == 0   5.2293    10.8048   0.484 0.628399    
## 1993 - 1990 == 0   6.0938    10.8048   0.564 0.572760    
## 1994 - 1990 == 0   6.5591     9.7323   0.674 0.500343    
## 1995 - 1990 == 0  15.4608     9.7323   1.589 0.112150    
## 1997 - 1990 == 0  17.9977     8.7768   2.051 0.040306 *  
## 1998 - 1990 == 0  15.8573    10.9967   1.442 0.149301    
## 2000 - 1990 == 0  20.3304     9.7323   2.089 0.036712 *  
## 2001 - 1990 == 0  21.0731    10.9284   1.928 0.053820 .  
## 2002 - 1990 == 0  29.7201     9.7323   3.054 0.002260 ** 
## 2003 - 1990 == 0  32.0884     9.7323   3.297 0.000977 ***
## 2004 - 1990 == 0  37.8323    10.8048   3.501 0.000463 ***
## 2005 - 1990 == 0  35.6733     9.7323   3.665 0.000247 ***
## 2006 - 1990 == 0  44.2090    10.9284   4.045 5.23e-05 ***
## 2007 - 1990 == 0  39.0401     9.7323   4.011 6.04e-05 ***
## 2010 - 1990 == 0  44.0279     9.7323   4.524 6.07e-06 ***
## 2014 - 1990 == 0  47.0284     9.7323   4.832 1.35e-06 ***
## 2015 - 1990 == 0  48.4391     9.7323   4.977 6.45e-07 ***
## 2016 - 1990 == 0  40.3690     9.7323   4.148 3.36e-05 ***
## 2017 - 1990 == 0  55.3324     9.7323   5.685 1.30e-08 ***
## 2018 - 1990 == 0  56.8137     9.7323   5.838 5.30e-09 ***
## 1993 - 1992 == 0   0.8645    11.8233   0.073 0.941712    
## 1994 - 1992 == 0   1.3298    10.8521   0.123 0.902475    
## 1995 - 1992 == 0  10.2315    10.8521   0.943 0.345777    
## 1997 - 1992 == 0  12.7684     9.9890   1.278 0.201162    
## 1998 - 1992 == 0  10.6280    11.9675   0.888 0.374504    
## 2000 - 1992 == 0  15.1011    10.8521   1.392 0.164063    
## 2001 - 1992 == 0  15.8437    11.9683   1.324 0.185567    
## 2002 - 1992 == 0  24.4908    10.8521   2.257 0.024022 *  
## 2003 - 1992 == 0  26.8590    10.8521   2.475 0.013323 *  
## 2004 - 1992 == 0  32.6030    11.8233   2.758 0.005824 ** 
## 2005 - 1992 == 0  30.4439    10.8521   2.805 0.005026 ** 
## 2006 - 1992 == 0  38.9797    11.9683   3.257 0.001126 ** 
## 2007 - 1992 == 0  33.8108    10.8521   3.116 0.001836 ** 
## 2010 - 1992 == 0  38.7985    10.8521   3.575 0.000350 ***
## 2014 - 1992 == 0  41.7990    10.8521   3.852 0.000117 ***
## 2015 - 1992 == 0  43.2098    10.8521   3.982 6.84e-05 ***
## 2016 - 1992 == 0  35.1397    10.8521   3.238 0.001203 ** 
## 2017 - 1992 == 0  50.1031    10.8521   4.617 3.90e-06 ***
## 2018 - 1992 == 0  51.5843    10.8521   4.753 2.00e-06 ***
## 1994 - 1993 == 0   0.4653    10.8521   0.043 0.965802    
## 1995 - 1993 == 0   9.3670    10.8521   0.863 0.388055    
## 1997 - 1993 == 0  11.9039     9.9890   1.192 0.233378    
## 1998 - 1993 == 0   9.7635    11.9675   0.816 0.414596    
## 2000 - 1993 == 0  14.2366    10.8521   1.312 0.189562    
## 2001 - 1993 == 0  14.9792    11.9683   1.252 0.210724    
## 2002 - 1993 == 0  23.6263    10.8521   2.177 0.029472 *  
## 2003 - 1993 == 0  25.9945    10.8521   2.395 0.016605 *  
## 2004 - 1993 == 0  31.7385    11.8233   2.684 0.007266 ** 
## 2005 - 1993 == 0  29.5794    10.8521   2.726 0.006417 ** 
## 2006 - 1993 == 0  38.1152    11.9683   3.185 0.001449 ** 
## 2007 - 1993 == 0  32.9463    10.8521   3.036 0.002398 ** 
## 2010 - 1993 == 0  37.9340    10.8521   3.496 0.000473 ***
## 2014 - 1993 == 0  40.9345    10.8521   3.772 0.000162 ***
## 2015 - 1993 == 0  42.3453    10.8521   3.902 9.54e-05 ***
## 2016 - 1993 == 0  34.2752    10.8521   3.158 0.001586 ** 
## 2017 - 1993 == 0  49.2386    10.8521   4.537 5.70e-06 ***
## 2018 - 1993 == 0  50.7198    10.8521   4.674 2.96e-06 ***
## 1995 - 1994 == 0   8.9017     9.6537   0.922 0.356472    
## 1997 - 1994 == 0  11.4386     8.6427   1.323 0.185670    
## 1998 - 1994 == 0   9.2982    10.8340   0.858 0.390760    
## 2000 - 1994 == 0  13.7713     9.6537   1.427 0.153713    
## 2001 - 1994 == 0  14.5140    10.8343   1.340 0.180366    
## 2002 - 1994 == 0  23.1610     9.6537   2.399 0.016431 *  
## 2003 - 1994 == 0  25.5292     9.6537   2.645 0.008181 ** 
## 2004 - 1994 == 0  31.2732    10.8521   2.882 0.003955 ** 
## 2005 - 1994 == 0  29.1142     9.6537   3.016 0.002562 ** 
## 2006 - 1994 == 0  37.6499    10.8343   3.475 0.000511 ***
## 2007 - 1994 == 0  32.4810     9.6537   3.365 0.000766 ***
## 2010 - 1994 == 0  37.4688     9.6537   3.881 0.000104 ***
## 2014 - 1994 == 0  40.4693     9.6537   4.192 2.76e-05 ***
## 2015 - 1994 == 0  41.8800     9.6537   4.338 1.44e-05 ***
## 2016 - 1994 == 0  33.8099     9.6537   3.502 0.000461 ***
## 2017 - 1994 == 0  48.7733     9.6537   5.052 4.37e-07 ***
## 2018 - 1994 == 0  50.2545     9.6537   5.206 1.93e-07 ***
## 1997 - 1995 == 0   2.5369     8.6427   0.294 0.769119    
## 1998 - 1995 == 0   0.3965    10.8340   0.037 0.970807    
## 2000 - 1995 == 0   4.8696     9.6537   0.504 0.613959    
## 2001 - 1995 == 0   5.6122    10.8343   0.518 0.604454    
## 2002 - 1995 == 0  14.2593     9.6537   1.477 0.139653    
## 2003 - 1995 == 0  16.6275     9.6537   1.722 0.084997 .  
## 2004 - 1995 == 0  22.3715    10.8521   2.061 0.039256 *  
## 2005 - 1995 == 0  20.2124     9.6537   2.094 0.036282 *  
## 2006 - 1995 == 0  28.7482    10.8343   2.653 0.007968 ** 
## 2007 - 1995 == 0  23.5793     9.6537   2.443 0.014585 *  
## 2010 - 1995 == 0  28.5670     9.6537   2.959 0.003085 ** 
## 2014 - 1995 == 0  31.5675     9.6537   3.270 0.001075 ** 
## 2015 - 1995 == 0  32.9783     9.6537   3.416 0.000635 ***
## 2016 - 1995 == 0  24.9082     9.6537   2.580 0.009875 ** 
## 2017 - 1995 == 0  39.8716     9.6537   4.130 3.62e-05 ***
## 2018 - 1995 == 0  41.3528     9.6537   4.284 1.84e-05 ***
## 1998 - 1997 == 0  -2.1404     9.9082  -0.216 0.828970    
## 2000 - 1997 == 0   2.3327     8.6427   0.270 0.787230    
## 2001 - 1997 == 0   3.0754     9.9541   0.309 0.757356    
## 2002 - 1997 == 0  11.7224     8.6427   1.356 0.174991    
## 2003 - 1997 == 0  14.0906     8.6427   1.630 0.103027    
## 2004 - 1997 == 0  19.8346     9.9890   1.986 0.047072 *  
## 2005 - 1997 == 0  17.6756     8.6427   2.045 0.040841 *  
## 2006 - 1997 == 0  26.2113     9.9541   2.633 0.008458 ** 
## 2007 - 1997 == 0  21.0424     8.6427   2.435 0.014904 *  
## 2010 - 1997 == 0  26.0302     8.6427   3.012 0.002597 ** 
## 2014 - 1997 == 0  29.0307     8.6427   3.359 0.000782 ***
## 2015 - 1997 == 0  30.4414     8.6427   3.522 0.000428 ***
## 2016 - 1997 == 0  22.3713     8.6427   2.588 0.009640 ** 
## 2017 - 1997 == 0  37.3347     8.6427   4.320 1.56e-05 ***
## 2018 - 1997 == 0  38.8160     8.6427   4.491 7.08e-06 ***
## 2000 - 1998 == 0   4.4731    10.8340   0.413 0.679697    
## 2001 - 1998 == 0   5.2158    11.9191   0.438 0.661678    
## 2002 - 1998 == 0  13.8628    10.8340   1.280 0.200699    
## 2003 - 1998 == 0  16.2310    10.8340   1.498 0.134094    
## 2004 - 1998 == 0  21.9750    11.9675   1.836 0.066325 .  
## 2005 - 1998 == 0  19.8159    10.8340   1.829 0.067393 .  
## 2006 - 1998 == 0  28.3517    11.9191   2.379 0.017375 *  
## 2007 - 1998 == 0  23.1828    10.8340   2.140 0.032370 *  
## 2010 - 1998 == 0  28.1705    10.8340   2.600 0.009317 ** 
## 2014 - 1998 == 0  31.1711    10.8340   2.877 0.004013 ** 
## 2015 - 1998 == 0  32.5818    10.8340   3.007 0.002635 ** 
## 2016 - 1998 == 0  24.5117    10.8340   2.262 0.023668 *  
## 2017 - 1998 == 0  39.4751    10.8340   3.644 0.000269 ***
## 2018 - 1998 == 0  40.9563    10.8340   3.780 0.000157 ***
## 2001 - 2000 == 0   0.7426    10.8343   0.069 0.945352    
## 2002 - 2000 == 0   9.3897     9.6537   0.973 0.330725    
## 2003 - 2000 == 0  11.7579     9.6537   1.218 0.223234    
## 2004 - 2000 == 0  17.5019    10.8521   1.613 0.106796    
## 2005 - 2000 == 0  15.3428     9.6537   1.589 0.111987    
## 2006 - 2000 == 0  23.8785    10.8343   2.204 0.027526 *  
## 2007 - 2000 == 0  18.7097     9.6537   1.938 0.052612 .  
## 2010 - 2000 == 0  23.6974     9.6537   2.455 0.014098 *  
## 2014 - 2000 == 0  26.6979     9.6537   2.766 0.005682 ** 
## 2015 - 2000 == 0  28.1087     9.6537   2.912 0.003595 ** 
## 2016 - 2000 == 0  20.0386     9.6537   2.076 0.037917 *  
## 2017 - 2000 == 0  35.0020     9.6537   3.626 0.000288 ***
## 2018 - 2000 == 0  36.4832     9.6537   3.779 0.000157 ***
## 2002 - 2001 == 0   8.6471    10.8343   0.798 0.424803    
## 2003 - 2001 == 0  11.0153    10.8343   1.017 0.309296    
## 2004 - 2001 == 0  16.7593    11.9683   1.400 0.161422    
## 2005 - 2001 == 0  14.6002    10.8343   1.348 0.177792    
## 2006 - 2001 == 0  23.1359    11.8233   1.957 0.050370 .  
## 2007 - 2001 == 0  17.9670    10.8343   1.658 0.097248 .  
## 2010 - 2001 == 0  22.9548    10.8343   2.119 0.034115 *  
## 2014 - 2001 == 0  25.9553    10.8343   2.396 0.016591 *  
## 2015 - 2001 == 0  27.3661    10.8343   2.526 0.011541 *  
## 2016 - 2001 == 0  19.2959    10.8343   1.781 0.074912 .  
## 2017 - 2001 == 0  34.2594    10.8343   3.162 0.001566 ** 
## 2018 - 2001 == 0  35.7406    10.8343   3.299 0.000971 ***
## 2003 - 2002 == 0   2.3682     9.6537   0.245 0.806211    
## 2004 - 2002 == 0   8.1122    10.8521   0.748 0.454748    
## 2005 - 2002 == 0   5.9531     9.6537   0.617 0.537453    
## 2006 - 2002 == 0  14.4889    10.8343   1.337 0.181121    
## 2007 - 2002 == 0   9.3200     9.6537   0.965 0.334328    
## 2010 - 2002 == 0  14.3077     9.6537   1.482 0.138313    
## 2014 - 2002 == 0  17.3082     9.6537   1.793 0.072986 .  
## 2015 - 2002 == 0  18.7190     9.6537   1.939 0.052495 .  
## 2016 - 2002 == 0  10.6489     9.6537   1.103 0.269987    
## 2017 - 2002 == 0  25.6123     9.6537   2.653 0.007975 ** 
## 2018 - 2002 == 0  27.0935     9.6537   2.807 0.005008 ** 
## 2004 - 2003 == 0   5.7440    10.8521   0.529 0.596600    
## 2005 - 2003 == 0   3.5849     9.6537   0.371 0.710375    
## 2006 - 2003 == 0  12.1206    10.8343   1.119 0.263257    
## 2007 - 2003 == 0   6.9518     9.6537   0.720 0.471454    
## 2010 - 2003 == 0  11.9395     9.6537   1.237 0.216167    
## 2014 - 2003 == 0  14.9400     9.6537   1.548 0.121718    
## 2015 - 2003 == 0  16.3508     9.6537   1.694 0.090315 .  
## 2016 - 2003 == 0   8.2807     9.6537   0.858 0.391017    
## 2017 - 2003 == 0  23.2441     9.6537   2.408 0.016049 *  
## 2018 - 2003 == 0  24.7253     9.6537   2.561 0.010430 *  
## 2005 - 2004 == 0  -2.1591    10.8521  -0.199 0.842298    
## 2006 - 2004 == 0   6.3767    11.9683   0.533 0.594175    
## 2007 - 2004 == 0   1.2078    10.8521   0.111 0.911383    
## 2010 - 2004 == 0   6.1955    10.8521   0.571 0.568064    
## 2014 - 2004 == 0   9.1960    10.8521   0.847 0.396774    
## 2015 - 2004 == 0  10.6068    10.8521   0.977 0.328373    
## 2016 - 2004 == 0   2.5367    10.8521   0.234 0.815178    
## 2017 - 2004 == 0  17.5001    10.8521   1.613 0.106832    
## 2018 - 2004 == 0  18.9813    10.8521   1.749 0.080275 .  
## 2006 - 2005 == 0   8.5357    10.8343   0.788 0.430789    
## 2007 - 2005 == 0   3.3668     9.6537   0.349 0.727267    
## 2010 - 2005 == 0   8.3546     9.6537   0.865 0.386801    
## 2014 - 2005 == 0  11.3551     9.6537   1.176 0.239495    
## 2015 - 2005 == 0  12.7659     9.6537   1.322 0.186040    
## 2016 - 2005 == 0   4.6958     9.6537   0.486 0.626667    
## 2017 - 2005 == 0  19.6592     9.6537   2.036 0.041706 *  
## 2018 - 2005 == 0  21.1404     9.6537   2.190 0.028533 *  
## 2007 - 2006 == 0  -5.1689    10.8343  -0.477 0.633302    
## 2010 - 2006 == 0  -0.1811    10.8343  -0.017 0.986662    
## 2014 - 2006 == 0   2.8194    10.8343   0.260 0.794688    
## 2015 - 2006 == 0   4.2301    10.8343   0.390 0.696211    
## 2016 - 2006 == 0  -3.8400    10.8343  -0.354 0.723020    
## 2017 - 2006 == 0  11.1235    10.8343   1.027 0.304568    
## 2018 - 2006 == 0  12.6047    10.8343   1.163 0.244667    
## 2010 - 2007 == 0   4.9878     9.6537   0.517 0.605387    
## 2014 - 2007 == 0   7.9883     9.6537   0.827 0.407962    
## 2015 - 2007 == 0   9.3990     9.6537   0.974 0.330244    
## 2016 - 2007 == 0   1.3289     9.6537   0.138 0.890510    
## 2017 - 2007 == 0  16.2923     9.6537   1.688 0.091472 .  
## 2018 - 2007 == 0  17.7735     9.6537   1.841 0.065604 .  
## 2014 - 2010 == 0   3.0005     9.6537   0.311 0.755941    
## 2015 - 2010 == 0   4.4113     9.6537   0.457 0.647705    
## 2016 - 2010 == 0  -3.6588     9.6537  -0.379 0.704680    
## 2017 - 2010 == 0  11.3046     9.6537   1.171 0.241594    
## 2018 - 2010 == 0  12.7858     9.6537   1.324 0.185354    
## 2015 - 2014 == 0   1.4108     9.6537   0.146 0.883813    
## 2016 - 2014 == 0  -6.6594     9.6537  -0.690 0.490304    
## 2017 - 2014 == 0   8.3041     9.6537   0.860 0.389680    
## 2018 - 2014 == 0   9.7853     9.6537   1.014 0.310758    
## 2016 - 2015 == 0  -8.0701     9.6537  -0.836 0.403176    
## 2017 - 2015 == 0   6.8933     9.6537   0.714 0.475190    
## 2018 - 2015 == 0   8.3745     9.6537   0.867 0.385671    
## 2017 - 2016 == 0  14.9634     9.6537   1.550 0.121136    
## 2018 - 2016 == 0  16.4446     9.6537   1.703 0.088482 .  
## 2018 - 2017 == 0   1.4812     9.6537   0.153 0.878055    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

2. Stacked categories - Supplement? Uva Island

Only plots, not stats

Explore 4x5

Data4_5<-subset(cover, Location=="4x5")

Explore Uva chains

Data_Chain_Uva<-subset(cover, Location=="UvRf-Chains")

By transect

Mean Chains

Uva_1m2

Data_Uva12<-subset(cover, Location=="Uva_1m2")

By transect

Mean 1m2

Cover<-grid.arrange(Plot_45 , Plot_UvaChains, Plot_Uva1m2, ncol=1)

#ggsave(file="Outputs/Fig_S1.svg", plot=Cover, width=8, height=10)

3. Supplementary datasets (Canal del Afuera and Secas)

Import data

# Read Canal de Afuera data (Pocillopora 2014-2018) 
  Data_CanalAfuera <- read.csv("CoverData/CA_cover.csv", header=TRUE, sep = ",")
  #summary(Data_CanalAfuera)
  
# Read Secas data (Massives 1980-2018) 
  Data_Chain_SECAS <- read.csv("CoverData/Secas_cover.csv", header=TRUE, sep = ",")
  #summary(Data_Chain_SECAS)
  
  # Read Secas + Uva data (Massives 1980-2018) 
  Suplementary.masssives <- read.csv("CoverData/Massives_cover.csv", header=TRUE, sep = ",")
  #summary(Suplementary.masssives)
  
  
# Format color
  FILL <-c("#C77CFF", "#F8766D", "#00BA38", "#619CFF")

Pocillopora non-Uva (Canal de Afuera)

Pocillopora_CA <- ggplot(Data_CanalAfuera, aes(x=YEAR, y=Pocillopora)) +
  geom_boxplot(aes(group=YEAR), outlier.shape = NA) +
  stat_boxplot(aes(group=YEAR), geom = 'errorbar')+
  geom_point(colour="#A3A500", alpha=0.3)+
  stat_summary(fun.y=mean, geom="line", colour="#A3A500") +
  stat_summary(fun.y=mean, geom="point", shape=21, size=2, alpha=0.8, fill="#A3A500") +
  
  scale_y_continuous("Canal de afuera reef \n Pocillopora cover (%)", 
                     limits = c(-2, 90), breaks = seq(0, 100, by=20),
                     expand = c(0,0.1))+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1980, 2018, by=2), expand = c(0,0))+
  facet_grid(Location~., scales="free")+
  
  ggtitle("a.")+
  
  annotate("rect", xmin = 1982, xmax = 1983, ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 1997, xmax = 1998, ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 2015, xmax = 2016, ymin = 0, ymax = 80,  alpha = .2, fill="gray")+
  facet_grid(Location~.)
Pocillopora_CA 

  • LMER model
  Data_CanalAfuera$Year_F<-as.factor(Data_CanalAfuera$YEAR)

  model_CA <- lme(
    Pocillopora ~ -1 + Year_F, random = ~1|Transect, data=Data_CanalAfuera)
  summary(model_CA)
## Linear mixed-effects model fit by REML
##   Data: Data_CanalAfuera 
##        AIC      BIC    logLik
##   114.7784 118.3186 -52.38918
## 
## Random effects:
##  Formula: ~1 | Transect
##         (Intercept) Residual
## StdDev:    9.232427 4.216186
## 
## Fixed effects:  Pocillopora ~ -1 + Year_F 
##               Value Std.Error DF  t-value p-value
## Year_F2015 57.43305  4.143548 10 13.86084       0
## Year_F2016 57.00977  4.143548 10 13.75868       0
## Year_F2018 70.15725  4.143548 10 16.93169       0
##  Correlation: 
##            Y_F2015 Y_F2016
## Year_F2016 0.827          
## Year_F2018 0.827   0.827  
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -1.05091857 -0.65554034 -0.05954312  0.42760030  1.72437930 
## 
## Number of Observations: 18
## Number of Groups: 6
  anova(model_CA)
  plot(ranef(model_CA))    # Symmetrical scatter effects around zero?
  plot(model_CA)           # plot residuals vs fitted
  resnorm1 <- resid(model_CA)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(model_CA)))    # Coefficients of the model
  
  plot(model_CA, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(model_CA, Pocillopora ~ fitted(.), abline = c(0,1))
  
# Multicomp
    Year_F.emm<-emmeans(model_CA, ~Year_F)
    #contrast(Year_F.emm, "tukey")
    year_groups<-cld(Year_F.emm, by=NULL) # compact-letter display
    year_groups
    #write.csv(year_groups, "Outputs/CanalPocilloTukey.csv", row.names = F)
    
# Effect plot
  plot(emmeans(model_CA, ~Year_F), comparisons = TRUE) +
      coord_flip(xlim = NULL, ylim = NULL, expand = TRUE) + theme_bw() +
    theme(axis.text.x = element_text(angle = 90)) + 
    ggtitle("Model CA predictions")

  • Summary stats Pocillopora CA

Massives Secas

Massive_Secas <- ggplot(Data_Chain_SECAS, aes(x=YEAR, y=Massive)) +
  geom_boxplot(aes(group=YEAR), outlier.shape = NA) +
  stat_boxplot(aes(group=YEAR), geom = 'errorbar')+
  #geom_smooth(method = lm, se=FALSE, linetype = "dashed", colour="red")+
  #geom_smooth(span = 0.2, se=T, colour="darkgray")+ 
  stat_summary(fun.y=mean, geom="line") +
  geom_point(aes(fill=Transect), alpha=0.5, shape=21) +
  
  scale_y_continuous("Secas Island reef \n Non-Pocillopora scleractinians cover (%)", 
                     limits = c(-2, 80), breaks = seq(0, 100, by=10),
                     expand = c(0,0.1)
                     )+
  scale_x_continuous("", limits = c(1979, 2019),
                     breaks = seq(1980, 2018, by=2)#, 
                     #expand = c(0.1,0)
                     )+
  annotate("rect", xmin = 1982, xmax = 1983, ymin = 0, ymax = 70,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 1997, xmax = 1998, ymin = 0, ymax = 70,  alpha = .2, fill="gray")+
  annotate("rect", xmin = 2015, xmax = 2016, ymin = 0, ymax = 70,  alpha = .2, fill="gray")+
  #facet_grid(Location~., scales="free_y")
  ggtitle("b.")
Massive_Secas

  • LMER model SECAS
  Data_Chain_SECAS$Year_F<-as.factor(Data_Chain_SECAS$YEAR)

  model_Secas <- lme(
    Massive ~ -1 + Year_F, random = ~1|Transect, data=Data_Chain_SECAS)
  summary(model_Secas)
## Linear mixed-effects model fit by REML
##   Data: Data_Chain_SECAS 
##        AIC      BIC    logLik
##   1734.272 1796.924 -849.1361
## 
## Random effects:
##  Formula: ~1 | Transect
##          (Intercept) Residual
## StdDev: 0.0004912232 7.641786
## 
## Fixed effects:  Massive ~ -1 + Year_F 
##                Value Std.Error  DF   t-value p-value
## Year_F1975  1.891718  1.528357 231  1.237746  0.2171
## Year_F1976  0.898021  1.708755 231  0.525541  0.5997
## Year_F1977  1.621573  1.208273 231  1.342059  0.1809
## Year_F1978  1.679452  1.080712 231  1.554024  0.1215
## Year_F1980 18.183354  1.753146 231 10.371842  0.0000
## Year_F1983  0.385200  2.416545 231  0.159401  0.8735
## Year_F1997  0.225000  2.416545 231  0.093108  0.9259
## Year_F1998  0.904762  2.888324 231  0.313248  0.7544
## Year_F2000  0.000000  2.416545 231  0.000000  1.0000
## Year_F2002  0.158157  2.416545 231  0.065448  0.9479
## Year_F2003  0.500000  2.416545 231  0.206907  0.8363
## Year_F2004  0.300000  2.416545 231  0.124144  0.9013
## Year_F2005  0.200000  2.416545 231  0.082763  0.9341
## Year_F2010  1.200000  2.416545 231  0.496577  0.6200
## Year_F2015  0.264049  3.417511 231  0.077264  0.9385
## Year_F2018  0.070547  2.416545 231  0.029193  0.9767
##  Correlation: 
##            Y_F1975 Y_F1976 Y_F1977 Y_F1978 Y_F1980 Y_F1983 Y_F1997 Y_F1998
## Year_F1976 0                                                              
## Year_F1977 0       0                                                      
## Year_F1978 0       0       0                                              
## Year_F1980 0       0       0       0                                      
## Year_F1983 0       0       0       0       0                              
## Year_F1997 0       0       0       0       0       0                      
## Year_F1998 0       0       0       0       0       0       0              
## Year_F2000 0       0       0       0       0       0       0       0      
## Year_F2002 0       0       0       0       0       0       0       0      
## Year_F2003 0       0       0       0       0       0       0       0      
## Year_F2004 0       0       0       0       0       0       0       0      
## Year_F2005 0       0       0       0       0       0       0       0      
## Year_F2010 0       0       0       0       0       0       0       0      
## Year_F2015 0       0       0       0       0       0       0       0      
## Year_F2018 0       0       0       0       0       0       0       0      
##            Y_F2000 Y_F2002 Y_F2003 Y_F2004 Y_F2005 Y_F2010 Y_F2015
## Year_F1976                                                        
## Year_F1977                                                        
## Year_F1978                                                        
## Year_F1980                                                        
## Year_F1983                                                        
## Year_F1997                                                        
## Year_F1998                                                        
## Year_F2000                                                        
## Year_F2002 0                                                      
## Year_F2003 0       0                                              
## Year_F2004 0       0       0                                      
## Year_F2005 0       0       0       0                              
## Year_F2010 0       0       0       0       0                      
## Year_F2015 0       0       0       0       0       0              
## Year_F2018 0       0       0       0       0       0       0      
## 
## Standardized Within-Group Residuals:
##          Min           Q1          Med           Q3          Max 
## -2.379463717 -0.212198142 -0.075570702 -0.004047582  6.834475873 
## 
## Number of Observations: 256
## Number of Groups: 10
  anova(model_Secas)
  plot(ranef(model_Secas))    # Symmetrical scatter effects around zero?
  plot(model_Secas)           # plot residuals vs fitted
  resnorm1 <- resid(model_Secas)
  hist(resnorm1, xlab = "Residuals", main = "") # are residuals normally distributed?
  coef.m1 <- as.data.frame(coef(summary(model_Secas)))    # Coefficients of the model
  
  plot(model_Secas, resid(., type = "p") ~ fitted(.) | Location, abline = 0)
  plot(model_Secas, Pocillopora ~ fitted(.), abline = c(0,1))
  
# Multicomp
    Year_F.emm<-emmeans(model_Secas, ~Year_F)
    #contrast(Year_F.emm, "tukey")
    year_groups<-cld(Year_F.emm, by=NULL) # compact-letter display
    year_groups 
    #write.csv(year_groups, "Outputs/SecasNonPocilloTukey.csv", row.names = F)
    
# Effect plot
  plot(emmeans(model_Secas, ~Year_F), comparisons = TRUE) +
      coord_flip(xlim = NULL, ylim = NULL, expand = TRUE) + theme_bw() +
    theme(axis.text.x = element_text(angle = 90)) + 
    ggtitle("Model Secas predictions")

  • Summary stats Massives Secas

Figure S2: Massives Uva+Secas

Figure S1: Percentage of cover by other scleractinian coral (non-Pocillopora) in Uva Island (top panel) Secas Island (bottom panel) reefs. Uva Island Non-Pocillopora scleractinian cover was <3.2% of the benthos across datasets and years. Secas Island was the only site with a significant cover of massive species before 1982-83 ENSO 18.2% (± 25.5 sd). However, the cover was reduced to 0.4% (± 0.7) after the 1982-83 ENSO and has not recovered up to 2018 (massive’s cover <1.5% in all the surveys between 1983 and 2018).

Other Supplementary figures cover

Packages used

Auguie, Baptiste. 2017. GridExtra: Miscellaneous Functions for "Grid" Graphics. https://CRAN.R-project.org/package=gridExtra.

Genz, Alan, and Frank Bretz. 2009. Computation of Multivariate Normal and T Probabilities. Lecture Notes in Statistics. Heidelberg: Springer-Verlag.

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